Yes, it would work. No, it's not a good idea.
Access would be able to handle the load, as long as those 35-40 people aren't all trying to access the database at once. It'll quickly bog down when you start having more than a couple of concurrent users, particularly if those users are all trying to update something.
The problem is that isn't not safe. You need to have the entire database file accessible on a network share, where any users will be able to write to it. You'll have multiple instances of Access trying to read and modify the file at the same time, and unless you are very careful with locking, it's quite possible for the database to become damaged or corrupt.
You'll also never be able to add any kind of access control beyond basic file permissions. You might not need it now, but internal databases often end up needing to be exposed to the wider world somehow.
It's not worth it. There are plenty of real RDBMS systems out there, for free, that are designed to handle this kind of thing. Why spend time trying to make Access work in such an environment, when you could just install SQL Server Express and be done with it? It has limitations, but if you're seriously considering Access, you're never going to be anywhere near those. Or use MySQL, PostgreSQL, Firebird...