It will just pile up in the mempool until some miners decide to include it within their block.<>There's nothing really magical on having 1000s of these transactions being done in a single minute, though the numbers would pile up on the mempool and the miners would have to clear it at some point.
If somebody would indeed spam the network with 1000 transactions a minute, even if they are not zero or near-zero fees they will have no chance of getting confirmed except maybe for the first ones, ever. The mempool nodes have is not unlimited, most nodes have the default limitations at 300MB so once transactions exceed that, the ones with lower fee will be simply dropped if an avalanche of 60k tx per hour or 1,5 mils a day hits the mempool so .....nothing happens!
But, why do something like the OP is thinking of in the first place, I see nothing to gain from it. If you want to hurt the network spam it with 100sat/b fee...if you can afford that for more than 2-3 days!
