"O" stated (in a recent classroom briefing) that while having a "sponsor" was NOT required, it would put the applicant at a great disadvantage compared to those who do have one.
The % of those called for interview without "sponsor" is VERY low, but not zero.
He also stated that the company was putting the "normal" hiring/interview process "on hold" for May and June in order to resurrect the Purple Nugget program and focus on filling the ANC slots.
His words (loosely quoted) - "we are selecting candidates for interviews who have MD11 experience and/or military heavy international experience" (I took that to mean KC-10 or equivalent experience/training)
FWIW - YMMV