Modern hardware is totally able to execute hundreds of thousands of transactions per second on a single core. If your query is simple and you can organise getting the data from storage at the necessary speeds you should totally be able to do this many requests, possibly even tens of millions.
But handling one million queries per second is completely different from having database server making progress on one million queries in parallel. What happens is, the database server is only making progress on a small number of them (typically in tens up to hundreds on a very beefy hardware) and everything else is just queued up.
There are much, much better ways to queue up millions of things than opening a million connections to get each one done individually.