Hi Roy, and welcome to the forums! The short answer here is no, it will not work easily to open or use MS Access database files, or to run MS Access itself. There are various things you can try... but Linux is not Windows, and it is not designed to run Windows programs. If you use the latest-greatest MS Access, you can just about forget about it. If older versions of Access will work with the files you need, there is some chance of running Access in Linux using a "compatibility layer" called
Wine. This makes Linux kind of pretend to be Windows, but it is far from perfect, so your mileage may vary. To give you an idea of what the Wine project says they can do with Access, take a look at
this page. Click on each version to see what works and what doesn't. Wine is free to use, but there is a paid program called Crossover Linux that may have better luck. I still would not be too hopeful here.
There are some Linux programs that may can convert Access databases into other formats, but you did not express an interest in that, so I won't search out those possibilities. Google will know more than I do anyway.
What may be your best option is to use Linux as a host operating system, and then install Windows as a virtual machine and run the real MS Access inside of that. Again though, there may be conflicts or things I'm not aware of that might still be a problem. This doesn't save you any money.... you'd still be buying Windows and still be buying (or subscribing) to MS Office.
Maybe others will have some better ideas. There are some fine database programs/tools available for Linux, but compatibility with MS Access formats has never been a very good option.
Good luck!