Pretty much what revellinho said.
There are very few mechanicals that will stop a bike from being able to limp to civilisation - you can scoot or freewheel on a bike that has had fairly catastrophic failures.
However, it is best to avoid mechanicals and a good regime of maintainence and replacing parts in a timely manner will help with this.
As I said, there is very little that will stop a bike from being able to, at least, get to civilisation if not finish the ride.
It isn't something I worry about overly. I have never had a significant mechanical on a ride, but I do carry a reasonable selection of spares that would get me out of most issues. At minimum you want a couple of tubes (pump and levers) and some form of multi tool. Chain links are also useful (I have never needed one myself, but have saved other people's rides with them).
If some dramatic mechanical happened that really was ride ending, there is always going to be a way to sort things out and get back home. It may involve vast expense (taxi etc.) or lots of time, or both. But that is life.
It isn't worth worrying about too much unless you are getting regular issues, in which case, you need to look at the kit you are using and find something more suited to the purpose.
Mudguards - well, if the org asks for them, then do try and use them. If you don't have them, then just be sensible - if you have a filthy, wet behind, don't sit down in the cafe etc.