I'm betting it will not work to your satisfaction.
The aluminum skin will shield the antenna except for signals coming straight down and most satellites will not be straight above you. (You can mount it under fiberglass, however.
Picture a cone going out from the antenna through the hole you have made. That will be your reception area. Also, as your plane moves around on the longitudinal axis, you may lose signals from stations you have acquired.
I'm not a GPS expert, but I don't think that this installation will work well for you. Better to just put it up on the glareshield. My -6 had the antenna on the glareshield and it worked great.
My 2c worth.