Of Course, they Can!
Most usually, spent cards are preferentially picked up, in a not-obvious way, of course, and re-inserted into the used stack of cards in the order they were removed from the tabletop.
Then, mechanic's shuffle can generally preserve the "order", to a fair extent, of those cards thusly "stacked". Few run-of-the-mill dealers are able to do this effectively; however, distorting the random order of re-use of the cards can, and does, benefit the House.
Separation of aces & tens is a new one on me. The most common "stacking" routine I watch for is placing 6s, 7s, and 8s together in succession, which throws advantage to the dealer. Watching carefully in order to detect other manipulative techniques destroys the fun inherent in the game, for me, anyway. imp