I emailed Lutron support as well and got the following reply:
We appreciate your inquiry. The PD-5WS-DV is our non-neutral based Caseta on/off switch. This is ratings for all lighting loads, including fluorescents. It's rated for a maximum of 5A of lights and does require the shunt capacitor, model LUT-MLC, to be installed between the switched hot and neutral either at the light if you have access to the wiring or in the wallbox. If you find that you lighting load is more than 5A, swapping these out for LED's to decreased the wattage may be better for your application. We hope this helps! Please let us know if we can assist you further.
Each of my 10 T8s are 32 Watts, the CFL is probably 7 Watts, the LED tubes are maybe 12 Watts. Total around 340 Watts. By my calculations I'm well under 5 Amps so I should be good to go!
I'm still not clear why I need the LUT-MLC, but I guess I can try it without and install if I find any issues.