We hired a guy a couple months ago who had everything he needed except his county cert (California goes by county) he had already submitted his live-scan and was just waiting for it to hit the SDEMS office. Since he already had to have a LiveScan done for his ADL we were fairly certain he'd come back clean and wouldn't have trouble picking up his actual card within a week or two, our hiring process is ridiculously slow so not much chance of him not getting it unless the live scan kicked back. He had paperwork backing that he had submitted everything and was very put-together. He was also former .mil.
So, that said, it depends. Perform well, be well put together in your interview and prove that you're just in the waiting game and it may happen. Or it may not, the market is so saturated right now that they may just move on to the next guy and not want to deal with the headache.
TLDR: It depends.