Phase 10 rules on discard pile
Yes.  The rules say that you must draw a card and that you must discard a card as part of your turn. (At least my edition) It does not state specifically about not being able to discard the draw off the discard pile.

However, I do question it as a strategy.  If the card to be picked up from the discard does not help the hand, then there is a much greater probability that the card from the draw pile will help the hand.