the address looks like a legit real street address so i don't think they will care since it's not a PO box, but i'm wondering what hiring/human resources think of me using my mailboxes etc address on my apps/resume since i'm in the process of moving into a new apartment and it's nice have the MBE address being permanent regardless of where in the city i live

Simple answer this is not a problem don't spend your time worrying about it.

Well truthfully, as someone who frequently has to go through resumes, I don't think I have ever really contemplated someones address that hard. Generally I look at what City is listed and determine how far they are from the work site and that's it.

Address are not compared on employment bg checks to the credit report address or any other address.
No one would ever know it is a MBE address. As the other recruiter said, we care about how far you are from the workplace but the only time I've ever noticed an MBE address was when I had a friend who had the "same" address.