Normally not, that would be a very odd exception. If the Co content is low, the 2p1/2 peak may vanish upon too coarse baseline subtraction. Can you post a screenshot of the unsubtracted and subtracted spectrum?
It is not possible to have of a p orbital only one spin orbit emission. The distance between Co2p3/2 and 1/2 is about 15 eV with 3/2 at around 780 and 1/2 at 795. Make sure your window is large enough.