I run my battery powered Veloce pre/power into a regenerator. (PS Audio P10).
If there’s a 110v input then I can’t think of a technical reason why it shouldn’t be connected to the output on a regenerator, assuming it’s stable and suitably rated, etc.
It might not be necessary from the perspective of improving the sound, however. Assuming the AC is disconnected during use, and the device is operating fully from the output of the battery, then the regenerator isn’t going to be helping with sound quality, but it might be providing some protection from spikes and such.
In the case of my Veloce hybrid amps, they’re still drawing from the AC line during operation, so it makes a bit of sense to run them off the regenerator.