If you have that many to check or more, yes, you'd better check the transactions when they appear on your node. But remember blockchain reorgs do occur and in that case you should detect it, and check if it has a consequence for your treatment or not.
Otherwise, it's probably not going to take that much to check the transactions of 1000 address, I'd bet for something between 1 and 10 sec.
Since you will have to keep a log of your treatment anyway, the best is perhaps to do both: try to treat blocks as they come, and once in a while cross check the transactions of each of your adresses in case a reorg made you miss something or treat something that you should not have.
It is only graved in stone after 720 blocks, before that, surprises can happen, although statistically it seems very rare to miss a transaction or treat one that is not going to be included, it looks like there are scenario where this can happen. So you must adapt your treatment strategy for that. It depends on the purpose of your treatment. If you can wait, it is always easier, if you want to be synchronous with the blockchain info, then it is harder because there are multiple possibilities at the present time. It also depends on the risk you take.