He can and that is the intention I believe. Apparently the penalty doesn't carry over and you can use previously used engine components, so he will take 2 new components/units.
Yeah, they stopped that before the 120+ grid penalty McLaren got last year. Quota penalties don't add up anymore, so in theory you could get away with changing as many PUs as you could in a weekend.
Gearbox penalties are different though - for some reason (I guess ratio advantages) they have to be used in sequence.
Surely you can't take multiple new engines in one go. You'd just take 20 at the start of the season and have a fresh engine each time with only one race of a billion penalty points but rag each one to within an inch of their life at each meeting.
Practically speaking you'd only want to take 2 in one weekend. One in FP1 (a whole new PU change before FP2 is quite a challenge that they'd try to avoid) and another one installed for FP3 that you'd also use for qualifying and the race. They'd be able to change certain individual elements before FP2 and qualifying too I guess.
But you couldn't just say "well, we want this one, this one, this one and this one in addition to the ones we start with. Oh, the grid penalty is fine". I think it's when it drives out into the pitlane in an official session that it counts, so you can't preempt the engine changes - you have to install it and drive it in practice, qualifying or the race.
Also, as said above, you wouldn't get any in-season upgrades even if you could pre-choose PUs, as once a PU is allocated, that is pretty much it in terms of homologation.