The FIDE laws of chess say nothing about upside-down rooks. However, starting with upside-down rooks is silly and if your opponent complains that it is annoying, I would expect the claim to be upheld.
11.5 It is forbidden to distract or annoy the opponent in any manner whatsoever.
The proper way of dealing with a missing queen (or any other piece) needed for promotion is to stop the clock and call the arbiter for assistance. However, the upside-down rook tradition comes from less formal settings, or maybe lower-budget situations where no arbiters with spare pieces in their pockets are close at hand.
It is interesting to note that the USCF rules explicitly allow the use of upside-down rooks for promotion:
8F7. Promoted piece not available. If the desired piece is not available to replace a promoted pawn, the player may stop both clocks in order to locate that piece and place it on the board. A player who cannot quickly find such a piece may request the assistance of the director. It is common practice, however, to play using an upside-down rook for a second queen. In the absence of the player’s announcement to the contrary, an upside-down rook shall be considered a queen.
Just, Tim. US Chess Federation’s: Official Rules of Chess, 7th Edition.