Is it possible? Not really, but there is a caveat.
If you play an opening gambit (i.e. The Smith-Morra) and then proceed to trade equal material, there is a chance it will show up as 0 blunders and 0 mistakes in the chess.com analysis tool, but you've simplified down to a pawn endgame down a pawn (thus losing).
Additionally, you have to realize that the analysis tool analyzes at whatever depth you have set (and that is limited if you are a free member). That means that a move that isn't classified as a mistake in one analysis might be classified as a blunder when doing deeper analysis. In short, do not take it as gospel, but as a guide. There are also times where it will classify a move as inaccurate or a mistake when it is the most human way to convert a position (this often happens when you are in a winning position and your opponent leaves more material hanging - the computer wants to continue collecting material when you can just as easily simplify the position into a winning endgame, which is the human approach). A good example of this is when the computer will point out "Here you missed a forced mate in 10" when you had a 2-move tactic to win their queen and then simplify into a winning endgame.
This is all theory actually, I may have the move order wrong but this is all book moves.
Sure, but you can't say there are no mistakes in that game.
book moves are not considered mistakes by engines. But yes, "mistakes" were made.