Hello mates!
Will try to make the long story short :)
MP-BGP follows almost the same route selection and loop prevention rules as BGP unicast.
So there is no traffic between B and C as the iBGP rules play here – if Received form iBGP do not send to other iBGP (iBGP Split horizon). In other words If A sent route 10.1.1.0 /24 to both B and C – B and C never send this route to each other, unless you introduce Route reflectors in your topology. (You can make Confederation but no sense with only three routers.)
If you want to play with diverse paths or to make load sharing between next hops (After you have RR) – you need to take into account BGP attributes which will help you to choose one next hop over the other ones. But again – everything is simple if you consider the rules for BGP network design.
In your situation If link between Router A and Router B will broke Traffic will not pass automatically to Router B because of the described iBGP split horizon rules.
Take care and have a great day!