i'd advise going in with the expectation of his anxiety never getting better. of course in the best case scenario, he wouldn't be anxious at all after settling into his new home & with your dog whom he gets along with, but there's also the possibility of him having some lifelong behavioural issues from that anxiety.
if you're prepared for the possibility of that, and can handle a dog who can pull strongly on a lead, i don't see why you couldn't give him his forever home!