Is it possible to hand-solder a BGA without solder balls
Is it possible to do? Sure anything is possible. There are many examples of people hand soldering bga csp or wlp type packages. Some do it as a repair others do it for debugging. Mostly as dead bug style.

Is it practical? No. Depending on the chip the extra length of wire may cause issues especially with high frequency signals. Since you want to solder the chip back in place on the board, the amount of tinning and solder you add to the board and chip is crucial to ensure no shorts no cracks no uneven heating. You are liable to ruin the chip and board that way.