This question concerns two different games with the same rules except for one difference.
In Game A: The dealer deals himself two cards in order with the other players (one face up and the other facedown).
In Game B: The dealer only deals himself one card face up and only deals the second card after all players have made their decisions. (Note: If the dealer gets a blackjack, any double downs / splits are returned to the player and they only lose their original bet)
Do these games have the same basic strategy? Is one better or worse for the player?
I feel like in Game B, there might be some clustering (is that the right term?) considerations. For example, if I'm playing 1 on 1 against the dealer, and I have, say, a 14 against a dealer 7, then if I hit and get a 10, that's the same result as if a stood and the dealer got that 10 and made 17. Does this affect my decision since the card I'm drawing is the same card that would go to the dealer? I'm not saying that standing with 14 against a 7 should be correct but is the EV different in Game A vs Game B?
As Nij points out in comments, for a well shuffled deck, it doesn't matter when the dealer's second card is dealt, the probabilities remain the same. Here's a way you may be able to see why:
In a well shuffled deck, it's not necessary to deal cards off the top of the deck, you can deal out (unseen) cards from anywhere, in any order. So there is no change in any probabilities if we adopt a convention that the dealer takes his cards from the bottom of the deck and all players' cards from the top. Under this convention, it doesn't matter whether the dealer waits to deal his second card or deals it immediately, it'll be the exact same card in either case.