VFDs and UPSs rectify AC into DC, and then create a new AC signal. The output and input are completely independant. Whether it can handle 1-phase at all really depends on the design- specifically, the controls. The guts are simple, they can handle it, but the controls might consider it a fault and shut down as opposed to switched into a derated mode.
If the input is wye, it really doesn't matter hardware-wise if you go L1-L2 or L2-L3, etc, they're all identical.
If you put 1-phase into a 3-phase VFD, even if it's rated for 1-phase use, you're going to introduce extra ripple current onto the DC bus which can may the output a bit dirty. You'll have to derate the VFD, probably to about 57% of its original rating.
