Possible, yes. Practical, maybe.
I once wired up a 4 pack of AA batteries to replace a cell phone battery. The scary part is making sure the voltage and polarity are correct. Some flashes have ports for external battery packs, using one of those it would not be hard to create a matching battery pack since the input port is there and presumably you could find specs for voltage and polarity for the jack. Doing it to a flash with only a AA battery connection would require more work and be riskier IMHO. You would have to either solder wires onto the battery connection or make a 'slug' that fits into the battery compartment and has wires running out to the exterior.
You could also look into old, used, "potato masher" style flashes. Pentax made one
AF 400T and external battery packs were available I believe. Of course these would all be manual flash and would need a triggering mechanism, either radio or wired.
And here is a
link to a Shutterbug article describing how to make an external battery pack.