Yes. The pitcher and the DH are treated as two separate people even if they're the same person, so replacing him in one role doesn't affect the other one. It's rule 5.11(b)I could look this up but I'm sure someone here will know immediately: so when Ohtani reached to start the 7th, could LAA pinch run for him as a DH and still keep him in as a pitcher? I am guessing no but I know there is at least one rule that tried to separate the two roles.
However, in the event the starting pitcher will bat for himself, the player will be considered two separate people for purposes of Rule 5.11(a). In such cases, the manager should list 10 players on his team’s lineup card, and this player should be named twice – once as the starting pitcher and once as the Designated Hitter. Thus, if the starting pitcher is replaced, he can continue as the Designated Hitter (but can no longer pitch in the game), and if the Designated Hitter is replaced, he can continue as the pitcher (but can no longer hit for himself).