No different than the situation today with "spend all the coins in the first 10000 blocks, without knowing the private key; and hope that miners extend the chain without having or checking the block.
There is a difference.
Today
there is an algorithm which produces 'true' if a portion of data is valid block and 'false' otherwize.
Spending 1M Satoshi's coins without his signature is invalid.
Valid PoW block without segwit data is neigher 'true' nor 'false'. It can be either 'valid' or 'unknown yet'
There is a difference.
Today everyone can check the blockchain and say "WTF? This block is invalid" and nobody would argue.
Tomorrow they would say: "Sorry, man. Your client just doesn't have segwit-data. We also can not provide it to you, but we are sure that it exists somewhere so we will not reorganize the main chain."
The segwit data is not sent separately.
Why? One
can send block to the network to all nodes 0.12.x, 0.11.x etc, wait 30 seconds, and send the segwit data
Everybody will know the hash and content of future block, but nobody will know is it segwit-correct or not.