Crutchfield sells an amp bypass kit. I can't find a link for it, but they have an 800 number.
You bypass the amp for two reasons
1: It's crap, works well with the low power factory head unit, but with todays 30-40-50 watt receivers you don't need it.
2: With aftermaket amps, you do not want to amplify the signal that is going into the amp you bought.
I think there's some minor wire splicing. The kit gives a how to. And I'll let someone else with a better memory tell you how easy it is. I had an aftermarket HU already in my car when I bypassed mine. But you can do it!
Yes you can bypass after they remove the stereo IF THEY DON'T rewire your wiring. I would NOT let them remove/reroute/rewire (whatever) the factory wiring. Basically with your new stereo there should be: stereo speaker output to the bypass then from the bypass to the factory stereo speaker wire connection.
To feel the safest, I'd get the bypass, then have the unit installed with the bypass. Any confident installer should be able to do that with little if any effort.