Will the wheel work right when it is full of boats on one side but NO boats on the other side?

There is NO weight difference.

When a boat enters the caisson it displaces its own weight of water and effectively there is no change in the overall weight.

For example:
Each caisson (chamber) is full of water - say 400 tonnes each.

A boat of 10 tonnes enters caisson number one and it displaces 10 tonnes of water.

You can thank Archimedes for the principle behind this... :)

The total weight in the caisson is still 400 tonnes (10 tonnes for the boat and 390 tonnes of water) and is still in equilibrium with the other caisson which weighs 400 tonnes.