My PCB manufacturer only requires eagle board file, and not a gerber file is it fine to go about getting the board fabricated with him?
My manufacturer only requires eagle board file, and not a Gerber file

Run away!

The competency of these people is highly suspect.  This is not a real board house.  Any minimally competent board house in the world will accept Gerber files.

Some board houses try attracting hobbyists that don't really understand board design and all the Gerber and drill stuff.  These board houses will sometimes take Eagle board files as a additional service.

However, even that is not a good idea.  Eagle board files don't directly specify all the choices a real engineer makes when exporting Gerber files from Eagle.  Take a look at the Eagle CAM processor, and you will see there is choice over what Eagle layers end up on the silkscreen, which board layers to export at all, etc.

You should be the one making the choices and exporting Gerber files from your Eagle design.  It's really not hard.  It may seem intimidating at first, but it's part of the process you need to learn if you want to design PC boards.  

Once you can create Gerber and drill files, you can have your board manufactured at pretty much any board house in the world, including the ones that cater to hobbyists and would have taken your Eagle file.  You may even find that such a board house charges less when given Gerber files.  In other words, they charge a premium for using the Eagle board file, just don't feature that.  If you pass the intelligence test and can supply Gerber files, you get a lower price.