If I vacuum seal a food product like beef stew then boil it in the bag, would it keep un-refrigerated? I'm wondering if after vacuum sealing something then boiling it, if that would act as sterilization allowing the product to remain safe without being refrigerated.
No, definitely not. It's not possible to safely preserve meat by boiling alone.

The only way to do this kind of thing at home is with a pressure canner, which lets you reach higher temperatures to properly kill everything dangerous.

See for example the NCHFP advice on canning meats.