The alternator (stator windings) will cover the non ignition electrical loads but without the stability of the battery. Not sure how punishing this would be to the shunt regulator. The XT225 is a very reliable bike and designed to survive reasonable failures without shutting your down. Glad you made it safely home.
I only had a few miles to go, so was willing to risk it. It's not something I'd want to put my trusty Serow though for any longer than necessary.
92 XT225 - New: tank, bars, seat, locks, v shiny new back wheel (well, most of it) and a DT125X speedo.
2007 XT250 - with screen