Is Seafoam safe?

SeaFoam is a great product and will work fine on a problem that actually needs something like this. SF should not be considered a miracle in a can that solves every problem.
SF and/or any carbon that comes loose will hurt nothing.

Has anyone actually scanned this vehicle for codes or has this all been wild guessing?

There are a number of things that could cause low speed lurching but not enough info is known to even make a guess. Codes first and go from there.