Can .fbx files be associated with Maya so they can be opened from Unity?

What I mean is opening a file by double clicking in the project view. My team has switched to .fbx for compatibility reasons, but we lost a lot of convenience in the process. I’ve looked through the Preferences with no luck; the options seem relatively sparse. If this is possible, is it a Pro only feature?

No.

FBX files are not linked to a 3rd party programe. But you will get the same effect as if they are if you have Maya and Unity on the same machine and drag the Maya file into your assets instead of exporting an FBX. Unity will then export an FBX for you and always check if you updated the Maya file, if you have, it will export a new FBX to replace the old so you will get a very smooth workflow of jsut having to save in Maya and seeing the result in Unity.

BE WARNED:
If you are collaborating with someone, note that if you move the project to a computer without maya, I think you will run into problems with your assets.