I guess the answer from me is, "it'll probably work, but...". As has already been said, mechanical fixings would be the best solution (Especially since you've got 20mm ply in the wall) but I don't think I've seen anyone else ask, how large is this proposed coat hanger and how many and how heavy are the coats are you proposing of hanging off it? I personally reckon a 3" x 3" square of wood stuck to the wall with something like pinkgrip would hold up a single or even two hefty coats pretty easily. What's the worst that could happen if it doesn't work? Coats fall on the floor and possibly the paintwork on the wall gets a little messed up.
In an ideal world Osvaldd, fix it to the wall with some screws for a proper job. But you could probably get away with just sticking it if there's enough surface area on your piece of pine. If it fails, there's no harm done and no massive amount of time wasted.
I wouldn't bother with CT1, very overpriced and not particularly good. Some people swear by it but I haven't noticed a difference that makes it worth £5-10 a tube more than everything else for general work.
Not a definitive test, but I was surprised that practically the cheapest tube of the lot (Pinkgrip) held the brick in place on the wall the best.
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