Maybe I've misunderstood something, but to me it seems the question is:
Can I use a 2:1 "Bow/SLE" kite bar with a C kite ?
A pulley bar in "original terms" is a bar where the center lines are connected to a pulley on a single line mounted at the bar ends (but rear lines connected to the bar ends as usual, fixed) - so you get a bar without a CL and where you can hold the bar dead centered with one hand - great for wake and passes
This bar is 1:1 and will increase turning automatically when you pull hard to one side
But I assume you mean a 2:1 bar, when you ask about a "pulley" bar ?
And yes, you COULD use a 2:1 bar with a C kite, but I am pretty sure it will be waaaaay too heavy as you double the bar pressure, and C kites has a lot more bar pressure than all 2:1 bow kites because of the geometry.
Kindly, Peter Frank
"SLE" bar with pulleys:
Note - the pulleys are at the bar ends, so the bar is 2:1
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Pulley bar:
Note - the only pulley is at the center, so the bar is 1:1 and no chicken loop depower, but still a trim strap.