Are you asking if you can remain on a seniority list as a mechanic while working at a regional?
Sounds tough. You could do all the GA training and work as a CFI on a mechanic's (or FA's, or CSRs) schedule.
But for new-hire training at a regional you would need to take a LOA or lots of vacation. No regional is going to work with you at all on that, their programs are not set up that way and they can't be in the business of doing favors, otherwise everybody would want one. Legally they probably can't prevent you from holding another job but they would probably not be happy about it, especially if it created "issues" with your regional job.
On reserve you might get ten days off per month.
Once you get on the line and off reserve, it might be more practical if you can bid any schedule you need on the mechanic side. You would almost certainly need to live in base for BOTH jobs.
Fundamentally I think it would come down to how much flexibility you have on the mechanic side, ie seniority, and whether can you bid down to significantly less than whatever a normal schedule is.
Bear in mind that while there's no legal prohibition, the FAA and NTSB would take a very dim view of it if you were involved in a flying accident/incident immediately after having pulled a 12-hour mechanic shift on the back side. So you need some actual sleep in there too.