Let's say this ban passes the Senate, if a lawsuit is filed quick enough before it's in effect will it just be in limbo before the case is heard or will it go into effect maybe the later be retracted?

No way to know. Would be partly which court. My gut tells me they will go for the most damaging scenario.

Whoever filed the lawsuit would ask the court for an injunction to prevent enforcement until the courts decide the issue. In the case of the California magazine ban, the court granted the injunction, though they don't have to.

As someone who spent 50 years living in Ny dont expect courts to save you. They wont.