Most likely yes, I would like to know also what Damon thinks of Jon, who is not a born riverlander, and married his sister. But yes, as a knight I'd imagine he is on the force, though with war on the horizon I don't think that force will last to long!
House Wylde is from The Stormlands it seems. But I think you probably had to earn his respect unknowingly, since you know… Damon doesn’t belittle people and act too elitist out loud. I imagine due to the fact of Jon’s love for Damon’s sister being genuine might be a good factor in Damon thinking the character of Jon worthwhile.
Yeah, I imagine Damon will abdicate the position when war comes as well.
Also, I feel like this is one-sided since you haven't told me what your character would think of mine!