I've done some digging - as I was curious about this. The situation as far as I can tell is this.
If you want to connect from Access to MySQL - you can do that with the MyODBC driver. There is a good amount of material out there on how this is done and it is really a windows thing as opposed to a Linux thing. If you would like some pointers, let me know.
Since Access is file based, I think it would be necessary to have the .mdb file on some kind of shared storage that windows and linux could see. It is possible to bring the mdb file over onto linux and open it locally - but of course, then windows would not be able to open it.
I'm going to keep playing around with this, as it's pretty interesting. I thought I would just give you an update on what I had found so far.