What happens if I push a pawn to the 8th rank and press the clock before converting it to another piece?
Does it make a difference if it's Blitz or not?
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"If the player has moved a pawn to the furthest distant rank, pressed the clock, but not replaced the pawn with a new piece, the move is illegal." Source: Fide Laws of Chess taking effect from 1 January 2018 at 7.5.2.
If a move is illegal, it's illegal in Blitz, too. What can differ between Blitz and classical is what the penalty for an illegal move is.
Previously, in blitz/rapid a player making an illegal move would instantly lose the game.
However, January 1, 2018 revisions to FIDE Laws of Chess acted "to equalize the rules for classical chess on the one hand, and rapid and blitz on the other, with regard to the penalty for making an illegal move."
Before, in both rapid or blitz an "illegal move" (which includes moving with two hands, or not making a move and pressing the clock) would instantly lose the game in case the arbiter intervened or the opponent stopped the clock. Now, in the first instance it will lead to a time penalty and only if a player does it again, he or she loses—just like in classical chess.
Source for quotes on 1/1/2018 change: Peter Doggers, New FIDE Laws Of Chess For Blitz, Rapid Still Not Perfect
It's a good question, especially regarding the difference between time controls. The answer is yes, there is an important difference: in Blitz (and Rapid chess, which is a frequently overlooked time control also covered in the rules) the game is a draw if the arbiter observes that the illegal position remains after the failing promotion move:
A.4.4 If the arbiter observes both kings are in check, or a pawn on the rank furthest from its starting position, he shall wait until the next move is completed. Then, if an illegal position is still on the board, he shall declare the game drawn.
For reference: A position is illegal when it cannot have been reached by any series of legal moves. (article 3.10.3)
Of course, the opponent could claim a win before he makes his move. But if he makes a move and the pawn remains on the last rank, the observing arbiter shall declare the game drawn.
This is not possible in standard chess (where each player’s thinking time is at least 60 minutes) because the position immediately before the irregularity shall be reinstated, and the penalty is two minutes extra time to his opponent (or the player loses the game if this is the second illegal move).
Building on Jim Ratliff's answer that this would be an illegal move, the regulation says:
a. If during a game it is found that an illegal move has been completed, the position immediately before the irregularity shall be reinstated. If the position immediately before the irregularity cannot be determined, the game shall continue from the last identifiable position prior to the irregularity. Articles 4.3 and 4.7 apply to the move replacing the illegal move. The game shall then continue from this reinstated position. If the player has moved a pawn to the furthest distant rank, pressed the clock, but not replaced the pawn with a new piece, the move is illegal. The pawn shall be replaced by a queen of the same colour as the pawn.
b. After the action taken under Article 7.5.a, for the first completed illegal move by a player the arbiter shall give two minutes extra time to his opponent; for the second completed illegal move by the same player the arbiter shall declare the game lost by this player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves.