Yes. MySQL will handle that no problem.
I've built quite a few MySQL/PHP sites and at least one of them (to my knowledge) now has more than 50,000 user accounts with each user able to create up to ten different (medium-size) text reports to go with their account. Potentially half a million records... and the site is still nice and peppy. Runs fast runs good no complaints.
Also.. Access should NOT (in my opinion) ever be used in a production environment to run a business-critical web application. It was never meant for that in the first place (that's why Microsoft sells their OTHER database MSSQL for scads and practically gives Access away with their Office packages).
Access is meant for small personal databases or maybe even a small office-wide application but beyond that... it chokes.
That's my 2cents 😉