They are required to send them to all previous employers where you worked as a pilot. They may or may not get a response from part 91 employers.
Technically they don't have to wait for PRIA responses, since that data is for their information only, they are no set rules that say if XYZ happened at your last employer they cannot hire you. The PRIA system just wants them to have access to the info.
Many employers wait for the background check and PRIA before giving class dates or even CJO's, because they don't want to have to fire you if it turns up something you lied about.
There's far less risk of getting sued for not offering a job in the first place, than firing someone out of class who already quit his old job.
But some airlines don't care, it's on you to ensure they have all the correct info when they make their hiring decision. If something comes up later they'll be happy to fire you.