Does The Fallout Mod Manager update files automatically? Thanks.

As far as I know it does not, don't take my word for it. This thread would be better suited in the modding section.

If you mean update mods automatically then no. You have to do that yourself.

It updates nothing automatically, if I recall correctly. It allows you to open websites for files you've slapped directly to FOMM after downloading, easing the updating a bit.