Going back through every event set I have, which isn't to say I have them all completed, dangit, not a single one gave an Achievement. The one premium set I bought (Fry's) has an Achievement. I believe Carribean (premium) does as well, and you confirm that Summer Spirits (premium) carries an Achievement.
So no, I'm not positive, but research counts for something, right?
I'm not going to buy either of the current Weps sets as neither will help my build, but am debating on Boswell when it gets released. You can preview Boswell on TWE and TWCalc, but it's not yet linked into the Wiki and is unlikely to ever appear in TWDb.
Actually, there is a lot of sets from events which bring achievement when we get all of their items : like Alford or siringo (in a general way, all the sets where we have to reach a streak of at least 120 or things like that). Same with Lucky Clover, which can be hardly fully won for free, otherwise it's accessible only in nuggets, or blue soccer team's set etc etc. For sets exclusively in nuggets (even if only weapon or mount sets), it's also not rare that there is an achievement with it : spirits, you confirm for Fry, there's Soccer fan's set too ... I can't tell if it's like that for all of the "exclusively in nuggets" sets or not.
But here, it's exclusively in nuggets (we couldn't win these sets at all for free in the event) : they just have the name of free sets but aren't part of them; they are independent weapons sets. I don't see how we could conclude knowing all other sets seem to be either fully in nuggets (with sometimes an achievement with them), either with difficulties to be won in events and sold afterwards in nuggets (with sometimes an achievement with them -cf. Lucky clover), either for free and never sold in nuggets but easy to win (and here again with sometimes an achievement with them lol). And here, it seems even different : clothing + mount sets as usual, and weapons sets exclusively in nuggets. I think that's a first ? In any case, I don't see a matter for a conclusion here ...
But I guess I won't have an official answer, or at least not before the end of the sale : that's a pity to not have an answer while the sale lasts only 2 days, and it's been more than 24h since I've asked my question. But well, whatever; I'm not a nuggetter, I'm only using my free nuggets so no real money involved

. But if I heard afterwards there's an achievement if 3 weaps, I think I'll have a grudge against the team lol : cause if I want the achievement after that, I'll have to spend 450 nuggets more for the 3rd weapon, instead of 200 with the chest ...
And thanks for the information about the boswell weapon set, Caerdwyn : I didn't know there was going to be one. I think I'll pass, personally : I don't have enough nuggets for both sales

And I think this kind of set is very usefull when you farm a lot, which isn't my case.