Yes, it’s advisable to ask the power supply manufacturer if they require a Wye sourced set of AC Mains. The reason being is that it’s common, in electronic equipment, to have a set of surge suppressing devices (like MOVs) on the input mains which are wired in a Wye and grounded at the midpoint. When that midpoint is no longer referenced (like a Wye) to the 3 hot legs, bad outcomes are possible with spikes/transients on the incoming Mains. So a fully floating or corner grounded source can – but not always – be a problem.
If the load was a simple dumb motor, it would not matter at all that your 3 phase supply was floating w/ respect to some “zero point”. But things like VFDs and your power supply can be a different story because they might contain filtering and surge suppression circuitry in the front end.
Also as Larry points out, the NEC is going to want some type of grounding scheme present.
Lastly, the best solution here is (imo) a proper step-up Delta –> Wye transformer. Especially if this is a permanent thing and not something you want to test for 3 hours and then take apart.
tldr: I would vote for the right transformer.