Does XORing a random block into a layer of CBC encrypted message add some bit strenght?
In general: No.
You have to assume the attacker knows what you are doing. That's Kerckhoffs' principle.
If your random blocks are actually a real One-Time-Pad on top of the block cipher, then it would be stronger - but you could achieve the same without the block cipher. If all your blocks use the same pad, this is true if the length is 1 block,  the pad is truly random, only used once and communicated using another secure channel.
If you just mesh different things together to make it more complex - that does not add security at all.
As a side note: The IV in CBC is not secret. If you consider it secret, you need to clarify how the sender and receiver both know it. And following that - do you consider that secret as static and reuse it? That would violate the requirements of an IV.