I am wondering whether the hand which a player receives is completely determined by the way in which the deck is shuffled- that the permutation of the cards after they are shuffled completely determines the hand a certain player, and that the cards the player is dealt with aren't randomly chosen when the dealer draws from the shuffled stack of cards. I am asking so that I can answer probability questions about poker.
Combinatorically, it doesn't matter whether the shuffle occurs before any card is dealt or if the cards are constantly being shuffled, provided there's no observation made by anyone in advance of selecting each card (i.e., we can't force a reshuffle because we don't like the card we'd otherwise select). So imagine an online game where the deck is shuffled and cards are successively drawn without reshuffle. This results in completely the same mathematics as reshuffling the remaining cards after each card is dealt (without replacement, of course).
Personally I adopt the theory of "quantum mechanics of poker" and that the next card isn't determined until it is observed by someone. Of course a particular card could be ruled out if observed by someone else in the hand. But the wave function of a particular card doesn't collapse until observed.
Adopt this mentality and you're less likely to tilt because of external factors, such as seeing you would have hit your out after you fold. (Because had you called, the river card might have been different!)
I'm not 100% clear on your question, I can interpret it two ways, and I'll answer both ways.
Yes, assuming we're talking a clean casino shuffle, the deck will be sufficiently randomised but once the cards are shuffled, assuming also a fair deal (i.e. no card mechanics) and no mistakes the players will received the cards based on the order of the shuffle no change.
If you're talking about if we are doing special types of shuffles to ensure, as an example, that seat 1 always gets aces, yes this is possible. It's called card mechanics. Some people are very very good at this. They can shuffle the deck and end up with the exact order they want.
If we assume a person is not a card mechanic, regardless of how they shuffle the cards, as long as they have done a reasonable job of mixing the cards it should be random, and not able to predetermine cards.
There are draw poker games where the cards available to a player depend on how earlier players in the hand have drawn. This isn't the case for hold'em.
If you have a game where people might join or leave, then the number of players in a hand might be determined after the shuffle is completed. That would change the specific cards to players.
For a given number of players and a non-drawing game like holdem, the hole and community cards should be completely determined. But it is possible for dealing irregularities to occur that do not result in a misdeal, but modify which cards are used.
For probability questions, I'm assuming none of these affect what you were considering. But they can occur in real play.
It mostly depends on the game you might be playing, some games like stud and draw poker, rather a player drops out or stays in the hand can effect the cards A player receives, with omaha and hold-em games rather or not a player stays in the hand has no effect on the cards that will be dealt, nothing really effects the order of the cards, accept perhaps an optional cutting of the deck that is allowed in some games typically before the flop where the players deal the cards.