Do PWM solar controllers increase current?
Just the term PWM does not give enough information, it needs to be more explicit.

Some solar controllers use PWM but only to control the average power charging the battery, they do not attempt to store any energy during the cycle and are lossy

Some of those operate by shorting the PV array so the unwanted power is dissipated within the array. Others may disconnect the array in which case the array does not output any power when not required.

MPPT controllers use a DC-DC converter which itself uses PWM together with energy storage elements (inductors) to avoid energy loss. The energy is stored during part of the PWM cycle and then sent to the battery during the second part.

The average output current, in this case, can be more than the average input current but the power output cannot be more than the power input. Efficiency can be up to the high 90% region.