However, we can argue for a more general ability to use devices while cloaked.
I'm tempted to say no, because we've seen that the cloak draws a lot of power to maintain the field.
Have we? I'd argue we have seen the exact opposite: the power-starved BoP in ST4:TVH had little problem maintaining her cloak, and more of a problem maintaining her transporters. Also, whenever we see an actual cloaking device, it's a tiny portable unit that can be hooked up to random low-grade power systems such as the Cardassian "shuttle" in "Profit and Loss", and can even cloak itself without being hooked up to anything.
The "cloaks require lots of power" statement is just a theory that Spock throws in the air in "Balance of Terror". We have never seen any solid evidence that Spock would have been right in his wild guess.
Shields and weapons both go down while the ship is cloaked.
Only if the cloaking software tells them to. Romulans seem to prefer this setup, probably for the extra degree of stealth it offers. Klingon ships have been shown to deflect disruptor hits even after cloaking, as in "Redemption", and can keep their weapons hot under cloak and sometimes fire them without bothering with the seconds-long decloaking routine.
Even if you could power the tractors, it probably wouldn't be a popular use because it would give away your position.
Indeed. The same with firing your weapons - unless you can make a quick getaway after firing your volley. This was probably easier back in Kirk's days, where the E-A could not target Chang's BoP quickly enough even though the enemy ship regularly revealed her location by firing. TNG era fire control systems might be faster, explaining why Chang's fighting style has gone out of fashion.
There's little point in using tractor beams for hit-and-run, of course. Unless the ship doing the capturing was a juggernaut capable of reeling in her prey in a matter of seconds and then escaping the wrath of the prey's sisters. And indeed the ability to do things while permanently cloaked might best be incorporated in a big and powerful supership, which would have more difficulty in the "pop-up" style of cloak warfare than the nimble BoPs. (Just witness how Picard is able to hit the clumsy
Scimitar repeatedly after scoring one "ranging hit", and Shinzon has great difficulty shaking his nemesis off once thus exposed.)
Timo Saloniemi