Probably not, to be honest. Some tests he'll pass with flying colors, others he would fail hard. Definitely not grounds for euthanization (selective dog reactivity, high possessiveness, prey drive); they'd probably just decide that he needed to be worked with, especially if the shelter knew dogs.
Stranger handling
Pass, not a problem at all. He doesn't generally let strangers physically manipulate him and turn him over, clean his ears, etc. but basic handling isn't ever an issue.
Resource guarding
Hard fail. This is actually the big reason why I think he'd fail the overall shelter test - I'm not familiar with shelter workers but I know food and toy aggression can be a big issue for some people. I can take anything from him without a problem, but strangers and anyone else in the family? Not so much. He is very much not okay with dogs or random people touching him while he has a toy or food, though his response is usually just to growl and move away.
Prey drive
Fail...? He'll chase after strange cats indoors out of curiosity and give them a sniff, but lives with them peacefully. Outdoors he goes insane for cats, but can learn to ignore squirrels, birds, etc.
Getting along with other dogs
Probably a fail. His play style is nonexistent and mostly involves him sniffing, posturing, and correcting the other dog. He can play with me alongside another dog, and that's about as good as it gets. He's selectively dog reactive as well, but he is fine with group walks and being indoors with another dog after a proper introduction.
Getting along with kids
Definite pass, not a problem there. Still would not be recommended for a home with kids just because of his size and exuberance, and how excitable he is, but he likes them a lot.
Getting along with cats
Pass, again not a problem. He lives with two cats, did great with our youngest when she was a kitten, and we once brought in a random cat that showed up at our doorstep, and Trent decided he was his new best friend.
Strange/loud noises
Easy pass, nothing like that phases him (including thunder and fireworks).
Would you intentionally adopt a dog that didn't "pass" certain portions of the test?
Definitely depends on what portion of the test the dog did not pass. If any of the issues that came up was fear based, I would not adopt the dog. I also would not adopt a dog with noise sensitivities, and again this includes a fear of thunder storms and fireworks (the latter being a big deal here on the 4th).
At this time, I also don't think I can work with flat out dog aggression because I'm just not equipped to deal with it, and wouldn't want to put my dog in danger due to my own inexperience. Reactivity is fine, as long as the dog is confident (which she/he would need to be to live with Trent).
Prey drive I like, but cat/small animal killing? No. Not indoors, at least, because I own and will continue to have various small pets in addition to my dogs. Resource guarding? Not an issue though it depends on the context and the dog's temperament and nerves. Same goes for stranger danger.