Possible, certainly. Practical? Maybe not. The first thing I'd do is make sure the battery polarity is correct and that you didn't maybe stick in a 34 when it should have been a 34R, or maybe had the battery in backwards so the positive cable was connected to the negative battery terminal, etc.
Is any of the wiring obviously damaged, or was maybe the smoke just from a fusible link or maybe even a diode in the fuse/relay panel? Are you considering buying a new harness or just splicing in wire to replace damaged sections? If splicing in, make sure to match the wire gauge and use adhesive-lined shrink sleeving to protect the splices.
-Rod