I can speak from experience. Even if your ASP.net website only uses .NET libraries supported by Mono you are going to have a hard time getting it to run if its anything beyond Hello World.
You won't have to re-write much code but you will spend hours/days/weeks dealing with little issues with mod_mono/xsp/apache configuration and file permissions and error handling and all the little things that go into a large website. (Be prepared to spend a lot of time asking questions on serverfault :) )
The problem is that a lot of people don't use Mono for ASP.net websites and so there aren't as many people reporting bugs so a lot of things that are minor bugs go un-fixed for a long time.
