No problem

I've been at Bayarea for 20+ years and switched quite a few positions/companies, with no time gaps.

A few times, I already negotiated with my next employer, but current employer asked me to stay a few days/weeks longer for more smooth business continuity, then I did so. It helped my career reputation, and better work relationship. 

My two cents is that, a few weeks double paychecks might not be an issue at transition times, especially for us most labor level individual contributors.