A while ago, Mr. Ekted wrote that all themes are veneer. That, even for heavily themed war games, if you stripped off the designs and names, and played the game simply as hexes, tokens, and dice, you would not be able to tell what the theme was. You may be able to say that it is a war game, but not which war.
First of all, I expect that at least some themes can be discerned from the wording of the mechanics, the piece abilities, and the map structure. But I wouldn't swear to it.
In any case, Ekted is making too much of the division between theme and mechanics. You can't strip off the theme to a game and still have the same game, really.
The very way that you describe a mechanic gives it a thematic flavor. Taking a card from a pile might be "drafting", "collecting", "selecting", "purchasing", "accepting", or a host of other thematic names that gives a clue as to what the theme is.
Also, it is a Euro-gamer's perspective that NASCAR Monopoly is the same game as Atlantic City Monopoly, with a simple theme switch. But that is not necessarily true. The pictures, the flavor, the act of moving a car rather than a shoe around a board, have a lot to do with the feel of the game. The mechanics cannot simply be separated out from this experience.
The most you can say is that an individual mechanic cannot be limited to, or ascribed to, a specific theme. Listing the mechanics of a game are simply not enough to describe the game. The mechanics of Atlantic City Monopoly are not Atlantic City Monopoly or even Monopoly; they are only parts of the game.
Or at least, one could argue that.
The point is that taking out the thematic overlays and then claiming that the game's theme is no longer detectable is not really saying much, since the game itself has changed.