I would think it could be a challenge to get reliable, repeatable results. I too have run 2"+ bits with a 2-1/4 and 2-1/2 HP router with decent results. The PC690 is a little workhorse but at 11amps, spinning a 2" bit (and a cheap bit at that) could be asking a lot of it. I don't have trouble with mahogany trying to burn like cherry or maple so you could get some good results. I would give it a try and keep in the back of your mind that if it doesn't do well and starts wasting expensive material; the money you are saving by making your own doors could be put towards a router with a little more oomph! (I knew I could rationalize a new tool into this thread if I tried )
Any sufficiently advanced technology is indistinguishable from magic.
- Arthur C. Clarke