I have not used the GTM integration but have used ReadyTalk and a few others -- based upon that, it should not be a problem. There are certain core statuses that the webinar vendor will update as part of the integration (Registered, Attended, etc.) and you can't mess with these.
Adding new ones should be fine though.
Some people have the invite campaigns as separate programs, with a success of acheiving a registration. That could also be something to consider.
Justin Norris | Perkuto