Bonding in alkali metal complexes
The bonding of alkali cations to water, to EDTA, and to crown ethers is strictly electrostatic in all three cases, at least based upon QTAIM analysis$^{[1]}$ of representative systems.



For this analysis, I ran gas-phase quantum chemical optimizations on $[\ce{Li}(\text{12-crown-4})]^+$, $[\ce{Na}(\text{EDTA})]^{3-}$, and $[\ce{Na}(\ce{H2O})_6]^+$ using ORCA v3.0.3. (I can post the computation inputs/outputs if anyone is interested.) I also optimized $\ce{NaCl}$ as an additional system with uncontroversial ionic bonding. While the gas-phase results will poorly represent a variety of aspects of the dissolved species, I think they should capture well enough the characteristics of the wavefunction necessary to study the types of bonding involved. Other gas-phase calculations I've run on, e.g., $[\ce{Cu}(\ce{H2O})_6]^{2+}$ have optimized smoothly to the expected octahedral ligand arrangement, lending credence to this assumption.

Some notes on the optimizations:


Geometry optimization of $[\ce{Li}(\text{12-crown-4})]^+$ converged readily.  
For $[\ce{Na}(\text{EDTA})]^{3-}$, despite starting in a prototypical octahedral chelation geometry, the EDTA molecule immediately began to 'loosen its grip' on the $\ce{Na+}$, clearly heading toward a less compact configuration. In fact, one of the oxygen atoms actually discarded its bonding interaction with the $\ce{Na+}$ in favor of an intramolecular hydrogen bond.  I performed the QTAIM analysis on the last geometry obtained before ORCA reached its iteration limit in the geometry optimzation procedure.
Similarly, for $[\ce{Na}(\ce{H2O})_6]^+$, despite starting the optimization in a prototypical octahedral coordination geometry, the water ligands 'wandered' throughout the optimization process, in a fashion loosely reminiscent of a molecular dynamics run. As with the EDTA complex, I just chose the final geometry after the optimizer halted as the one on which I ran the QTAIM analysis.


For illustration, I generated GIF animations of the $[\ce{Na}(\text{EDTA})]^{3-}$ and $[\ce{Na}(\ce{H2O})_6]^+$ optimizations. The individual frames were produced with the 'Movie Maker' module of VMD 1.9.1 and the final GIFs were generated using EZgif.com.



Several metrics generated by QTAIM analysis argue for strictly ionic bonding of the alkali metal atoms in these systems:


Low electron density $(\rho \substack{&lt;\\\sim}0.1)$ and positive density Laplacian $(\nabla^2\rho&gt;0)$ at the relevant line critical points between the alkali cation and the coordinating oxygen (or nitrogen) atoms
High localization index $(\mathrm{LI}\substack{&gt;\\\sim}0.9)$ in the alkali atom basin
Low delocalization index $(\mathrm{DI}\substack{&lt;\\\sim}0.75)$ between the alkali atom basin and those of the coordinating atoms


Strictly speaking, in addition to $\#1$ above, the terms of the Laplacian perpendicular to the bond path must also be small in magnitude in order to diagnose ionic bond character$^{[2]}$, but I have omitted those values here.

The table below presents these metrics for the above representative chemical systems, as well as some reference molecules possessing uncontroversial bonding types.  Due to the fairly regular geometry of $[\ce{Li}(\text{12-crown-4})]^+$, the metrics didn't vary much throughout the system and I averaged them for each bond and atom type.  Despite the lack of a deep energy well, the metrics were also similar for the six oxygens in $[\ce{Na}(\ce{H2O})_6]^+$, so I averaged the values here as well.  For the irregular geometry of $[\ce{Na}(\text{EDTA})]^{3-}$, the values differed enough that I chose to report them indivdually; the numbering of the coordinating atoms is arbitrary.  All non-literature data were generated by MultiWFN v3.3.7 on Windows 7 using the default settings and the "Medium" grid for generation of the atomic basins for the $\mathrm{DI}$ and $\mathrm{LI}$ calculations. All values are in atomic units: $\rho\equiv{e^-\over\mathrm{Bohr}^3}$ and $\nabla^2\rho\equiv{e^-\over\mathrm{Bohr}^5}$ ($\mathrm{DI}$ and $\mathrm{LI}$ are dimensionless).

$$
~ \\
\textbf{QTAIM Results} \\
\begin{array}{ccccccccc}
\hline
\mathbf{Species} &amp; ~ &amp; \mathbf{Bond} &amp; \rho_\mathbf{LCP} &amp; 
    \mathbf{\left(\nabla^2\rho\right)_\mathbf{LCP}} &amp; \mathbf{DI} &amp; ~ &amp;
    \mathbf{Atom} &amp; \mathbf{LI} \\
\hline
 &amp; &amp;  \ce{Li-O} &amp; 0.036 &amp; +0.26 &amp; 0.077 &amp; &amp; \mathrm{Li} &amp; 0.922 \\
[\ce{Li}(\text{12-crown-4})]^+ &amp; &amp; \ce{O-C} &amp; 0.25 &amp; -0.50 &amp; 0.856 &amp; &amp;
     \ce O &amp; 0.870 \\
 &amp; &amp; \ce{C-C} &amp; 0.26 &amp; -0.70 &amp; 0.949 &amp; &amp; \ce C &amp; 0.656 \\
 &amp; &amp; \ce{C-H} &amp; 0.28 &amp; -1.01 &amp; 0.901 &amp; &amp; \ce H &amp; 0.420\\
\hline
&amp; &amp; \ce{Na-O}1 &amp; 0.015 &amp; +0.086 &amp; 0.064 &amp; &amp; \ce{Na} &amp; 0.974 \\
&amp; &amp; \ce{Na-O}2 &amp; 0.021 &amp; +0.131 &amp; 0.096 &amp; &amp; \ce{O}1 &amp; 0.899 \\
[\ce{Na}(\text{EDTA})]^{3-} &amp; &amp; \ce{Na-O}3 &amp; 0.020 &amp; +0.121 &amp; 0.089 &amp; &amp;
     \ce{O}2 &amp; 0.900 \\
&amp; &amp; \ce{Na-N}1 &amp; 0.014 &amp; +0.074 &amp; 0.056 &amp; &amp; \ce{O}3 &amp; 0.900 \\
&amp; &amp; \ce{Na-N}2 &amp; 0.018 &amp; +0.094 &amp; 0.065 &amp; &amp; \ce{N}1 &amp; 0.766 \\
&amp; &amp;  &amp; &amp; &amp; &amp; &amp; \ce{N}2 &amp; 0.769 \\
\hline
[\ce{Na}(\ce{H2O})_6]^+ &amp; &amp; \ce{Na-O} &amp; 0.014 &amp; +0.086 &amp; 0.057 &amp; &amp; \ce{Na} &amp; 0.975 \\
&amp; &amp; &amp; &amp; &amp; &amp; &amp; \ce{O} &amp; 0.916 \\
\hline
[\ce{NaCl}]^0 &amp; &amp; \ce{Na-Cl} &amp; 0.035 &amp; +0.197 &amp; 0.321 &amp; &amp; \ce{Na} &amp; 0.978 \\
&amp; &amp; &amp; &amp; &amp; &amp; &amp; \ce{Cl} &amp; 0.975 \\
\hline
[\ce{LiF}]^{0\,\ddagger} &amp; &amp; \ce{Li-F} &amp; 0.079 &amp; +0.749 &amp; 0.179 &amp; &amp; \ce{Li} &amp; 0.957 \\
&amp; &amp; &amp; &amp; &amp; &amp; &amp; \ce{F} &amp; 0.991 \\
\hline
[\ce{CH4}]^{0\,\ddagger} &amp; &amp; \ce{C-H} &amp; 0.291 &amp; -1.168 &amp; 0.980 &amp; &amp; \ce{C} &amp; 0.661 \\
&amp; &amp; &amp; &amp; &amp; &amp; &amp; \ce{H} &amp; 0.469 \\
\hline
^\ddagger~_{\text{Values from Ref. [2]}}
\end{array}
$$

As can clearly be seen, the interactions between the alkali metals and the ligating atoms are uniformly of ionic character: low electron density and positive Laplacian at the LCP; low $\mathrm{DI}$ between the paired basins, and quite high $\mathrm{LI}$ for the alkali metal basins. This is consistent with the ionic species $\ce{LiF}$ and $\ce{NaCl}$ in the table, and is in marked contrast to the covalent systems included.




$^{[1]}$ More information can be found on Wikipedia and at RFW Bader's page at McMaster University.  A more readable (but unfortunately paywalled) description is provided in Ref. [2].
$^{[2]}$Bader &amp; Matta, Found Chem 15: 253 (2013). doi:10.1007/s10698-012-9153-1.