1. Yes, they will - or would - put a strain on the power grid if those facilities were just added to the current grid with no additional supply, but of course that's not the case. The utility companies, Entergy and MS Power at least, are always and now more rapidly trying to expand what they can supply. It's very expensive and time consuming, so there may be some times where it's difficult to keep up. But they are working on it.
2. Most (or at least a large portion) of the new tech/industrial power-sucking users, like data centers, are working on 'off-grid' solutions for the future. So they are trying to save cost and be outage-proof by building their own sources of power. There are many ways to do that, with varying success and reliabilty so far. But it's a ways off for most of them, because that is an even more costly and time-consuming step - and those users have to pay for it themselves without being a public utility who can raise rates, etc. Same thing can be said for water supply too - many of the users are working on ways to keep their water usage in a self-contained internal cycle as much as possible in the future.