CFL bulbs using more watts then rated
Yes, that will have a big effect on it.  If you're familiar with the difference between Watts and VA... that. 

Watts and VA normally differ when the load has poor power factor, but it could also be when the output is not sinewave and the load wants sinewave (e.g. a motor). 

Perhaps it is drawing the correct wattage (or VA) but your tester is misreporting due to not knowing how to handle non-sinewave supply.