Can I leave Japan while waiting on my visa?

I'm applying for my Nikkei Sansei visa and plan to submit everything once my background check comes in from the FBI in about 2 weeks hopefully, but I have a trip planned to the US for 2 weeks in November/ early December. I am worried that my application won't be done by that time. Am I allowed to travel and come back? Will it affect my application? (I am currently SOFA status but that will be gone once I apply for the visa and I get a 30 day temporary stay.)

by voiobyalp