Question: given that clutch-less shift is executed properly, does it
take a toll on transmission in any way?
See Rory's answer: it is possible to do properly without wear. It is difficult to do properly every time.
For example: does clutch-less shifting reduce life of synchros?
While you are learning shift clutch-free, yes, you will beat the hell out of the synchros.
My advice is to learn how to properly heel-and-toe using the clutch (and actually double clutching). Become an expert at using the clutch properly and then decide whether clutchless shifting is for you.
Full disclosure: I never shift without the clutch. I don't drive a dog box in competition and don't see a good reason not to use one of the pedals available to me. I've worn through the floor mat in two places trying to become better at heel and toe-ing, though.