After the fork they will most likely get banned as soon as they try to relay blocks over 1 MB to you (someone that actually read the code please correct me if needed).
So Shorena, they may be banned by pereira4, but is that not the point at which the Bitcoin network splits in two, as all the classic nodes accept the larger block and the core nodes are still looking for the next block?
The network is split with the fork, yes. One side is accepting blocks over 1 MB size (up to 2 MB) while the other side is rejecting these blocks as invalid and will ban nodes that consistantly send invalid blocks. Its most likely not an easy cut, but more like a messy tear as some blocks (those smaller than 1 MB) will still be valid on both sides. Due to the 750/1000 blocks needed for activation and the grace period it is however unlikely that there will many core nodes left afterwards.
Is it possible to currently run a node and broadcast a 2MB block?
Yes, it will not get accepted by your peers though.
You will not get banned for sending one invalid block, but if you consistantly do so, your peers will ban you and you will have lost the connection to the network.