I would not count on it. I expect unclaiming physical cards and trading them so they can be claimed by another will be the only trading available.
I'm basing that on the fact that it appears we get some currency (the skulls) from getting extra copies of cards we already have plenty of, and that leveling up cards seem to level the whole stack of them even if you have more than a single playset. Those both seem like ways to mitigate getting too many copies of certain cards.
Is there trading in Heartstone? How about Lightseekers? In Solforge we never got trading, instead we got the opportunity to burn our cards for crafting points, then the ability to craft specific cards from those points.
You can trade all your physical cards, just unclaim and trade with ur friend with photo, and then he claims it.
Check out this thread.
I've unclaimed a few cards and took a picture to send it to people to trade digitally, yes there is the issue of someone taking it without the trade or money but its like anything really, except more risky. So be careful who you trust