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Generally speaking, no it won't work, unless there are some equipment tricks I don't know about. You mentioned using a ground as neutral. If you do that, then you'll only have 120V potential. If you use one of the three phase legs as a neutral and another as the hot, you'll have 208V potential. That might work since it sounds like you're dealing with something that is relatively voltage insensitive. I'll reluctantly admit that I've done this before in a couple of restaurants.z
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Huh? How do you get 208V out of a 240V three-phase system? In short, you don't.
I'm an electrical engineer - I work with three-phase stuff all the time. There are two types of three-phase connection, Wye and Delta. In a Wye (4-wire) system there are three hots, a neutral and a ground. Neutral and ground are bonded together at the distribution panel. In a Delta (3-wire) system there are three hots and a ground - phase to ground voltage in a Delta system depends on how the ground is connected to the transformer. (There are ungrounded Deltas but they are not legal to set up today.)
By far in commercial systems the 4-wire Wye is most common. Then there are three normally commercially available voltages, 208V, 240V, and 480V. In 208V systems the hot-to-neutral is 120V, phase-to-phase is 208V, and it is used in distribution systems where some 3-phase is needed, but the majority of the loads are 120V single-phase. In 240V systems the phase-to-neutral is about 138V (not useful), phase-to-phase is 240V. This is used in systems where the load is primarily three-phase, or where a lot of 240V single-phase is required. In 480V systems the phase-to-neutral voltage is 277V, phase-to-phase is 480V, and this is used where the load is primarily three-phase (though there are 277V single-phase lighting systems, usually found in industrial buildings).
Trust me, I do this stuff for a living. I even have a license.