No. More importantly... never consider using unlicensed content in anything you produce. The negatives just outweigh the positives.
Public Domain: This is 75 years from the death of the writer... if a corporate entity doesn't renew the copyright. I can almost promise that a corporate entity still owns the HB music catalog.
If you're doing a no-budget project consider Moby Gratsi or Kevin McCloud or other creative commons material. This may become problematic if you plan to acquire distribution or if this is a corporate venture. Honestly though... stock music is so cheap these days, why not just license something from a production music catalog?
While it is, admittedly, a rare thing, there are cases where a work falls into the public domain by default because there's no one left to claim the copyright on it. I'm trying to figure out whether or not that's happened here. Is there a search engine or anything where I might be able to find that out? Does anyone know? Anyone? Bueller? Bueller?
EDIT: Further research has uncovered the answer. The music cues in question are from the Capitol Hi-Q production music library. According to the US copyright office, if a work published before 1978 does not include a copyright notice somewhere on the packaging, then it's not copyrighted. Period. Looking at the record sleeve via a google image search, the Hi-Q library has no such notice. On that basis, I am assuming that it is safe to use.