When looking for a PhD advisor, will it matter if I send them an updated version of my masters thesis?
There are no strict rules about this, so you should do what is in your own best interest: send them the best version you have available.
However, you should consider that your potential PhD supervisor may talk to your the supervisor of your master's thesis. It is possible they will discuss the thesis, and it could cause lots of confusion if they unknowingly are talking about different versions. Therefore I would recommend to let your prospective PhD supervisor know that you have sent them a version you updated after your graduation.