Conventional wisdom has always been to NOT be employed by two companies at once. I have heard of people being let go after their new employer (major) finds out they're still employed by a regional while in ground school.
If you want to preserve the option to return to the old employer, I would try to take vacation if allowed. But I'd also discuss with both new and old employers...make sure nobody is going to consider this fraudulent. The military routinely allows this (terminal leave) and airlines are OK with that but I wouldn't just assume the same principle applies to a civilian employer.
Ideally airlines (esp. regionals) would have snap-back policies allowing pilots who leave for another airline to return to their previous position and seniority within 90 days or so if the are involuntarily terminated from the new job. A few regionals used to do this IIRC. Only fair given the way the seniority system is a rigged...you might have to put ten+ years seniority on the line in order to "try out" for a new job.