Does an inspector guarantee the shield stays up fully and at all times when a tinkerer is also present at the same outpost?

tried it. No. If the inspector is hired after the tinkerer the shield charges fully but then depletes. The description of the inspector is fairly explicit but one can hope...

Combine him with a navigator and you could leave/return every time you wanted it back to full shields I guess.

Yep. Yet another reason navigator is awesome.

Realistically though, I usually see people combine tinkerer and queen and leave their queen with no shields with no ill effects.