In overwhelming majority of cases, the best players play regardless of the parent's role or participation level in the booster club. There are, of course, exceptions. That depends on the character of the coach.
Joining the booster club is a good idea. Then you can participate in some of the group decision making, or at least make your opinions known as a legitimate member of the club. Many booster clubs distribute info by email these days. Policy may exclude non-members from the email list - just speculation there.
Here's a scenario for you. A very successful local HS baseball team has a booster club with several levels of membership fees ranging (as I recall) from $25 to $500. Members who buy in at the lowest level are not allowed voting privileges on booster club business.