There are hard limits to Access's internal engine (JET, IIRC) which you're likely to run into as time goes on. The unfortunate thing is that there isn't anything you can do to avoid the limits or recover once you've hit them.

On the other hand, you can install Postgres under Windows and then build an Access frontend over ODBC. This gets you the best of both worlds, IMO, at the cost of running a kind of odd stack. Cheaper than SQL Server though, and I like the maintenance story better.

TBH the last time I considered a solution like this I was consulting, so it was a few years ago, and all my clients either didn't sign up at all or went for a custom web solution instead, so I don't have a lot of war stories about this platform. I do think it would work though.