Yes and not, you surely can develop successfully with mono on linux, but .NET is not "write once, run everywhere", is more a "write once, run everything" framework.
It's heavy tangled with all the Microsoft and Windows technology and promote the reuse of code in that ecosystem.
That's a rather unique take, given how Xamarin has managed to build a massively successful company around the idea of using .NET to target non-Windows platforms.
+ core = standard library, io/string/async/thread/etc/linq.
+ some bundled stack, like wcf for create service, wpf for ui, mef for plugin, xml serialization, json serialization, asp.net webforms, etc.
Mono try to reimplement all.
Runtime and standard library work very well on mono.
bundled stacks can work, work partially or not implemented, depends (on contribution, check mono website). Some stack are really old way to do things, deprecated, usefull only on windows.
Also Microsoft for new stacks (like asp.net MVC) try to open source, so mono need to compile source and fix bug/different behaviour, not rewrite
If you use a library who depends on a bundled stack, can or cannot work on mono.
Library who depends on open source or standard lib, should work