As I see it, full nodes are there to verify the miners block and propagate blocks to other full nodes.
Miners can act as full nodes, if not they do not they risk the chance of mining a block with an invalid transaction.
What would happen if the miner mined a block, and there were no full nodes to validate it?
Full nodes are more useful than simply for block propagation, and miners are not the only type of user on the Bitcoin network that benefits from validating the whole blockchain themselves. I would argue that anyone who wants to ensure they aren't being tricked should be running a full node, such that they can be truly trustless. This group should probably included exchanges, merchants, and even individual users (to some extent).
As for your question about what would happen...well...nothing. The miner would find a valid hash for a block, and then propagate it to nobody. Nobody would check it against their blockchain, and nobody would pass it on other nodes (of which there are none). SPV nodes wouldn't receive block headers, nor would anyone respond to their bloom-filtered requests for transaction updates. There would be nobody to send them to.
Bitcoin is a network, which consists of nodes and paths. When you take away the nodes, the paths cannot exist. You are effectively asking "if there was no Bitcoin network, how would the Bitcoin network operate?" Simple answer: it wouldn't.
Your question basically boils down to "if a tree falls in the forest, and nobody is there to hear it, does it make a noise"? Of course blocks with invalid transactions would still be invalid, but if nobody consumes the blockchain, nobody would notice.
The Bitcoin network's backbone is made up of full nodes. Its product is the creation of a consistent state across all participants in the network. If there are no participants, the network would be pointless regardless whether the information were valid or invalid.
