People say you can tell whenever there's a buy because price will tick up, but wouldn't there also be times when there's a buy but there's a larger amount of liquidity at that price point than was absorbed by the buy and therefore price doesn't go up?

Short answer is yes; you are quite right that whether a price ticks up/down depends on the amount of resting orders in the order book at that price level. A large number of orders will absorb a small market order without necessarily moving the price.