Is this necessarily so?
We know that no cloak is perfect. Narratives have always made it possible to detect cloaked ships. In "Balance of Terror," it was when the Romulan ship passed through a comet. In STIII, there was some visible distortion visible to the naked eye. In STVI it was impulse exhaust. In "Redemption II," Picard set up a tachyon grid. Etc.
If there are sporadic emissions of any kind from a cloaked ship...
... then using a cloaked ship to infiltrate Romulan space would be a rather dubious proposition in the first place, since every minute the Klingons spend in orbit raises the chances of their being detected. If the ship gets detected, the Romulans destroy it and probably declare war on the Klingons for violating their space.
It's just more likely, in context, that the Romulans aren't unaccustomed to seeing Klingon ships operating in Romulan space and wouldn't think there was anything particularly threatening about a bird of prey being near Romulus. To the extent that the Klingons and the Romulans seem to be engaged in a Cold War of sorts -- and the fact that Sela and her people were able to come and go from Qo'nos with relative ease -- it's more likely that the Klingons and the Romulans BOTH have ships orbiting each other's homeworlds, that both sides are tracking (or, with varrying degrees of success, trying to track) each other's surveillance vessels, and that they generally avoid actually FIRING on a lurking Klingon/Romulan ship because neither side can really afford to have their cold war go hot. So the Klingon ship in "Unificiation" was probably on and off their radar the entire time, with Romulan controllers monitoring it (as best they could) figuring it to be another Klingon surveillance bird. Not, by itself, particularly threatening, but also not particularly welcome.
Granted, even just one ship might carry a weapon of mass destruction capable of annihilating a capital planet or rendering it uninhabitable.
Sure, but again there's the fact that the Romulans have their OWN ships in orbit of Qo'nos who are in a position to retaliate in kind if the Klingons try it. So they're both sitting there with their cloaked daggers at each other's throats, wondering which of them will make the first move. In this case, the cloaking device doesn't make EITHER of them undetectable, just untargettable; more importantly, since any starship must decloak before it can fire its weapons, a cloaked ship can be considered slightly less threatening than a visible one. Should a Klingon or Romulan vessel suddenly become VISIBLE in orbit of the other's homeworld, they would probably destroy it instantly, but as long as you remain cloaked, they're just watching you (or your shadow) with their finger on trigger.
Starfleet, however, doesn't go in for this cloak and dagger bullshit. You enter Federation space in a cloaked ship, you've just volunteered for an ass whupping. If you're lucky, they'll stick a photon torpedo up your ass and watch it light up your engine room from the inside out. If you're unlucky, they'll zap you with an phase modulated tachyon pulse that causes your entire crew to hyper-evolve into Jim Hensen abominations and then mail you back to your homeworld in tiny cages.
In the weird and paranoid world of cold war politics, then, it makes sense that Picard and Data would have used a Klingon ship to infiltrate Romulus; the Romulans don't consider cloaked Klingon ships to be a threat, and IF they get caught, the Klingons can believably shrug and say "Don't look at us, we had nothing to do with that."