You have to test these yourself. Potentially the problems that can crop up are:
- Improper registering of COM DLLs -- you have to test your application installer to make sure this doesn't happen
- Registry complications - some third party components set registry entries that can only be entered using their own installer, rendering it impossible for you to properly install the component yourself. In that case you have to bootstrap their installer to yours.
- Unknown dependencies -- if your third party components have dependencies to other components that are not obvious
- Unknown requirements -- if your third party component has specific hardware requirements, they might fail.
- Unclear environment requirements -- some third party components can run on Windows Server 2000 or 2003, but not on 2008, or vice-versa
All of these can be mitigated by testing your final application installer on vanilla (plain-Windows) servers which represent a good sample of your targeted server OSs: Windows Server 2000, 2003, 2008. You should also test your application against freshly-installed instances of IIS 5, 6, and 7.
Consequently, if you wish to target Mono, you have to make further tests on various Linux distros.