Does boron form compounds without covalent bonds?
Boron can form ions but there is some fine print.  You won't get monatomic cations like the metals below it.  Instead, ionic boron structures are formed from clusters where the ionic bonding is driven by the molecular orbital structures in these clusters, not by electronegativity (cf. This answer).
Such clusters are internally held together by covalent bonds between the boron atoms, so in this sense boron is still forming covalent bonds.  The ionic bonds would be with atoms of other elements outside the boron cluster.  Since the valence shells of a neutral boron atom are less than half filled the clusters will likely have low-energy, bonding orbitals that require electrons from outside atoms.  Thus the boron clusters will be anionic and the ionic bonds will be most likely formed with electropositive metals.  As suggested in the comments, magnesium diboride, $\ce{MgB2}$, is one of the most widely studied compounds containing such boron clusters. It has drawn much research interest because of its relatively high critical temperature (39 K) for superconductivity, which may be related to the impact of ionic magnesium-boron bonding on the eletronic interactions that lead to superconduction.
Magnesium diboride has a layered structure in which magnesium layers alternate with boron layers.  The latter are covalently bonded into a hexagonal honeycomb, resembling a carbon layer in graphite.  However, in the boron layers each atom supplies only three electrons per atom instead of four, so the layers may act as electron-accepting structures to form macro-anion having the formula $\ce{B^-}$.  An ionic model for the diboride would then have the empirical formula $\ce{Mg^{2+}(B^-)2}$.  Here I discuss two references I have examined, in which the bonding is examined and the results may be compared with this model.
De la Mora et al. [1] compare magnesium diboride with other $\ce{MeB2}$ diborides using early transition metals and aluminum (the latter might also be regarded as having early-transition-metal character, as there is no $d$ block separating this element from magnesium).  They find that while all the diborides have significant ionic character, this ionicity is enhanced in the magnesium compound.  Thereby the magnesium compound has increased electrical-conduction anisotropy as the valence electrons are strongly localized towards the boron layers.  Zirconium diboride, with less ionic bonding and less electron localization, is also superconducting, but its critical temperature according to this reference is only 5.5 K versus 39 K for the magnesium compound.  The authors also suggest that an isoelectronic, even more strongly ionic $\ce{Li(BC)}$ compound may offer an even further enhancement in superconductivity.
Nishibori et al. [2] found that at room temperature, magnesium is essentially fully ionized to $\ce{Mg^{2+}}$ while the boron remains neutral; the negative charge is associated with the interstitial regions as if to constitute metallic bonds.  This still represents two-thirds of the theoretical charge separation for an ionic model and in that sense, the bonding between magnesium and boron may be deemed predominantly ionic.  At 15 K the electrons become more localized so the boron now has a significant negative charge and the percentage of theoretical charge separation exceeds 80%.
Thus both references agree that in magnesium diboride, the combination of an electropositive electron source with a favorable molecular structure for electron acceptance leads to strongly ionic bonding between the magnesium and the boron.  This applies especially in the low-temperature superconducting state, even as the boron-boron bonding within the boron layers themselves remains covalent.
References
1.
Pablo de la Mora, Miguel Castro and Gustavo Tavizonb,
&quot;Comparative study of the electronic structure of alkaline-earth  borides (MeB2; Me=Mg, Al, Zr, Nb, and Ta) and their normal-state conductivity&quot;, Journal of Solid State Chemistry 169 (2002) 168–175, https://doi.org/10.1016/S0022-4596(02)00045-2.
2.
Eiji Nishibori, Masaki Takata, Makoto Sakata, Hiroshi Tanaka, Takahiro Muranaka and Jun Akimitsu, &quot;Bonding Nature in MgB2&quot;, Journal of the Physical Society of Japan 70:8 (2001), 2252-2254,
https://doi.org/10.1143/JPSJ.70.2252.