What kind of marshall is it?
I can't see you ruining anything, at least you won't ruin the drums electronics. As for the amps, you might wanna use 'common sense' when dialing in the low end eq on the bass amp. That kick drum probably delivers lower frequenzies than a bass guitar, not sure of the specs.
As for your marshall, depending on type, the main 'issue' I guess will be quality of sound. If it has a line in, use it, maybe you are able to get something undistorted out of it at listening volume. Some recent (MG series) marshalls have issues and break down easily, but this specific setup is new to me.