I'd have to lean towards a no. As other people have said, there isn't enough of a card pool to support it right now (the fun of it in Hearthstone is you have no idea what you get, whereas now you can pretty much predict what you get. But even with more cards, I'm not entirely sure that Gwent's mechanics suit unconstructed play.
So with only 5 classes, the only way picking a random class would work would be giving a selection of 3 or so random leaders to choose from, and then you get the faction of that leader . You'd have to limit deck size to get an equal draft, lets say to 25. So then you pick your 15 bronzes from your faction (I'm assuming in a similar manner to Hearthstone, so you get a selection of 3 cards and you pick one, repeat 15 times). It wouldn't be fair (or balanced) if one side gets more golds than the other so then you have to pick 6 silvers and 4 golds for your last 10 cards. With all that structure in place you are left with what is basically going to be a constructed deck, but without some of the synergies (any card with a muster ability, for instance, is never going to get picked because you can't guarantee getting all 3). Golds are going to have to synergise well with the deck - you have to pick them last, imagine if you picked Isengrim and proceeded to get no special cards, for example. At that point, its just a deck that's as constructed as just putting in any deck what you get from your random kegs anyway. The only way its a different experience is if you include cards from any faction in your draft, and at that point its just going to get confusing, and not work together at all.
Maybe that comes too much as Hearthstone is my only real point of reference - I'd rather not see them rip off that game too much, the reason Gwent is good is because its NOT Hearthstone. I'd love to see new modes added to the game, I just feel that Gwent has to be at least semi-constructed.
So with only 5 classes, the only way picking a random class would work would be giving a selection of 3 or so random leaders to choose from, and then you get the faction of that leader . You'd have to limit deck size to get an equal draft, lets say to 25. So then you pick your 15 bronzes from your faction (I'm assuming in a similar manner to Hearthstone, so you get a selection of 3 cards and you pick one, repeat 15 times). It wouldn't be fair (or balanced) if one side gets more golds than the other so then you have to pick 6 silvers and 4 golds for your last 10 cards. With all that structure in place you are left with what is basically going to be a constructed deck, but without some of the synergies (any card with a muster ability, for instance, is never going to get picked because you can't guarantee getting all 3). Golds are going to have to synergise well with the deck - you have to pick them last, imagine if you picked Isengrim and proceeded to get no special cards, for example. At that point, its just a deck that's as constructed as just putting in any deck what you get from your random kegs anyway. The only way its a different experience is if you include cards from any faction in your draft, and at that point its just going to get confusing, and not work together at all.
Maybe that comes too much as Hearthstone is my only real point of reference - I'd rather not see them rip off that game too much, the reason Gwent is good is because its NOT Hearthstone. I'd love to see new modes added to the game, I just feel that Gwent has to be at least semi-constructed.