The GFCI breaker will see the imbalance, and trip. Remember that the GFCI is looking at the difference between the current on the hot and the neutral on the load side of the GFCI.
I've seen a similar installation with a split outlet below the kitchen sink. Split wired, with one side switched for a disposal (fed from a GFCI breaker), and the other side unswitched for a dishwasher (fed from a separate circuit),
using a shared neutral.
It went unnoticed for almost 20 years, until somebody actually tried to use the dishwasher circuit. The GFCI would trip every time, with a very small load on the non-GFCI side. The problem was compounded by the fact that the bathroom on the other side of the wall was also fed from the GFCI circuit, while the second bathroom shared a non-GFCI circuit further down the wall. The solution was to install GFCI outlets where needed, and remove the GFCI breaker.
You will want to run 2 wires for each circuit.
