I’m actually not sure. They’ve been allowed for IFComp, and you can publish free to play games on itch, but not certain about entering other comps with prize money. You might need to email COG as the staff don’t monitor every post here. (I’d be interested to know also.)
There is a compile feature built into the CS package (like the quicktest feature). I’m not sure if it’s working since the firefox stuff? Can try it and see. Sometimes you need to rename the file it creates with an .html extension for it to play properly.
Alternatively, I know I’ve used CSIDE to compile games for itch. (And you can also use it to include scene created images if you need to.) It’s under export-> compiled game
This thread has some info on how to publish CS games to itch, and compiling with the built in program (starting at about post 27 onwards)