EDTA titrations of singly charged cations
Titrations involving chelating of metal ions with ethylenediaminetetraacetic acid (EDTA) is an extremely useful analytical tool and a very well studied system in analytical chemistry. It can be bind to virtually any metal ion, evidently even to alkali metals. For instance, sodium ion complexes with EDTA in certain situations (Ref.1). The abstract of the reference states that:

The crystal structures of tetrasodium (1,2-ethanediyl-dinitrilo)tetraacetate pentahydrate and disodium dihydrogen (1,2-ethanediyldinitrilo)tetraacetate dihydrate have been determined. $\ce{Na}$ ions prefer to act as bridges between different $\mathrm{edta}$ ligands and only in the tetrasodium salt is the $\mathrm{edta}$ ligand hexadentate to one $\ce{Na}$ ion. $\ce{Na}$ ions display seven-coordination, when coordinated to one $\mathrm{edta}$ ligand (distorted pentagonal bipyramid), and six-coordination, when linked to several $\mathrm{edta}$ ligands (from distorted octahedral to trapezoidal bipyramidal geometry). An $\ce{Na}$ ion in the tetrasodium salt shows five-coordination, because the sixth site is blocked by the $\mathrm{edta}$ ligand. $\ce{H}$ atoms in the disodium salt are linked to amine groups. Only these two salts can be obtained on varying the $\mathrm{pH}$ of an aqueous solution containing $\ce{Na+}$ and ethylenediaminetetraacetic acid. The first is obtained around $\mathrm{pH}$ 2-5 and the second around $\mathrm{pH}$ 12.

Nonetheless, there are no evident in the literature that EDTA titrations can be done to determine alkali metal concentration (agreeing with M. Farooq in his comment). As a matter of fact, disodium ethylenediaminetetraacetate (dihydrate) salt is the EDTA source it has been almost always used in most of EDTA titrations to determine  a large number of metal cations including alkaline earth and transition metals. Keep in mind that $K_f$ values of alkali metal complexation with EDTA are very law compared to other metals (Ref.2):
$$
\begin{array}{|c|c|c|c|}
\hline
\text{Cation} &amp; K_f &amp; \text{Cation} &amp; K_f &amp; \text{Cation} &amp; K_f &amp; \text{Cation} &amp; K_f\\
\hline
\ce{Li+} &amp; 6.17 \times 10^2 &amp; \ce{Be^2+} &amp; 1.58 \times 10^9 &amp; \ce{Cr^2+} &amp; 3.98 \times 10^{13} &amp; \ce{Sc^3+} &amp; 1.26 \times 10^{23}\\
\ce{Na+} &amp; 4.57 \times 10^1 &amp; \ce{Mg^2+} &amp; 6.17 \times 10^8 &amp; \ce{Mn^2+} &amp; 7.41 \times 10^{13} &amp; \ce{Y^3+} &amp; 1.23 \times 10^{18}\\
\ce{K+} &amp; 6.31 \times 10^0 &amp; \ce{Ca^2+} &amp; 4.90 \times 10^{10} &amp;\ce{Fe^2+} &amp; 2.09 \times 10^{14} &amp; \ce{La^3+} &amp; 3.16 \times 10^{15}\\
\ce{Ag+} &amp; 2.09 \times 10^7 &amp; \ce{Sr^2+} &amp; 5.37 \times 10^8 &amp; \ce{Co^2+} &amp; 2.04 \times 10^{16} &amp; \ce{In^3+} &amp; 1.00 \times 10^{25} \\
\ce{Tl+} &amp; 3.47 \times 10^6 &amp; \ce{Ba^2+} &amp;  7.24 \times 10^7 &amp; \ce{Ni^2+} &amp; 4.17 \times 10^{18} &amp; \ce{Bi^3+} &amp; 6.31 \times 10^{27} \\
\hline
\end{array}
$$
This lack of complexation of alkali metals with even strong chelator such as EDTA can be attributed to their lower Lewis acidity (EDTA is a strong Lewis base because it contains both amino and carboxylate groups).
Apart from alkali metal cations, singly charged transition metal cations form  complexes with chelates and can be determine by relevant titrations. For example, concentration of silver(I) ions ($\ce{Ag+}$) can be determined by cyanide titration (a monodentate):
$$\ce{Ag+ + 2CN- -&gt; [:\!N#C-Ag-C#N\!:]-}$$
The fairly high $K_f$ values for those singly charge cations (e.g., see the values for $\ce{Ag+}$ and $\ce{Tl+}$ in the table above) other than alkali metals suggest that they were able to involve in complexation titrations (They are compatible with alkaline earth metals).
References:

M. Font-Bardia, X. Solans, M. Font-Altaba, “Sodium ion complexes with ethylenediaminetetraacetic acid,” Acta Crystallographica Section C 1993, C49, 1452-1456 (https://doi.org/10.1107/S0108270193001350).
Arthur Earl Martell, Robert M Smith, Editors, In Critical Stability Constants, Volume 1; Plenum Press: New York, NY, 1974, pp. 204-211 (ISBN-13: 978-0306352119).