The print is larger than standard mat board size but you can get them custom made.
If you don't use mat board then you need spacers as you suggest. Spacer material is quite expensive.
If you want to do it on the cheap then you can join the mat board.
Frankly, it will look a lot better with a mat board surround than just filling the frame. That sort of looks like a poster.
The frame is going to be a significant cost anyway.
I don't know where you are but I'm in Australia.
You can get some indication of what it will look like on the Quote and Simulation Tool at http://AspirationImages.com