I don't think you can just go straight from not giving a free kick, to giving a dropped ball under the guise of playing the advantage. Normally, in a position like that if you think it's a foul, you should give it. As others have said, it's not clear there'd really be much of an advantage to be gained anyway
But I think it's also somewhat a question of sequence and timing. Let's say for instance, that you see what you think might have been a foul on the keeper but decide to let it go because the keeper has the ball and looks like they're going to clear the ball upfield (which is kind of like playing the advantage, in a way). However, after taking a few steps and getting close to the penalty mark, the keeper starts feeling the after-effects of the challenge and goes down, still holding onto the ball. You pretty much have to stop play then, let the keeper get the required attention and then you would indeed restart with a dropped ball to the keeper.
In fact, I'm wondering if the question was prompted by almost this exact situation in the Man City vs Man Utd WSL game last week. Utd keeper Mary Earps delayed picking up the ball as a City player approached (Georgia Stanway, IIRC). The City player made a move towards the ball and it looked like she may have caught the keeper's ankle. The referee didn't react one way or the other and I suspect she didn't see the incident as a foul or at least, not one worth calling. When the keeper went down injured a few seconds later, the referee stopped play and called for the trainer. Play restarted afterwards with a dropped ball to the keeper.