Interesting topic. I hope that a thread about cheater detection doesn't get locked automatically, though.
I believe the method you describe should work quite well, though I've never tried it. One could even do a simple plot of move perfection over time to see if an engine were being used, and at which periods of the game the engine were used. (If someone pays me enough and provides the source code for the analyzer, I'll add graphics and even measurements of the suspiciousness.) By running the analysis against some of the most popular engines, one could even determine exactly which engine had been used for the game.
To detect a likely cheater, download the pgn file(s). Open the pgn using Babaschess, available as a free download. Go to Edit > Analyze Game > Analyze. Use Ctl-f to flip the board if needed. At the top of the list of moves, select the two-column list view. Scanning down the list of moves, you can easily see when a person has played a perfect or near-perfect game using computer assistance. You can see very clearly the difference between a person's games when they do or don't cheat. A few more observations: They sometimes use the computer after getting into some trouble, and suddenly play perfectly after that, or they play perfectly up to a point of having a significant material advantage and then begin playing without assistance. Finally, it's clear that people don't really improve their game by cheating. If they want to improve their game, then just play against the computer.