I'd double check but from memory Quarq cranks are the ones with the long spindle so should be fine with a BSA frame. I have the non PM force BB30 cranks in a BSA frame myself, still room for a BB and a few spacers
I had a look. SRAM-Quarq cranks are BB30 and Bb386 compatible. For Bb386 you need a long spindle as it's an 86.5mm shell, exactly what you get with a BSA shell + external cups.
I'd double check but from memory Quarq cranks are the ones with the long spindle so should be fine with a BSA frame. I have the non PM force BB30 cranks in a BSA frame myself, still room for a BB and a few spacers