Unlikely, since screens & shields reduce this possibility.
I feel I have to comment on this, at least in regards to TOS. One gets the distinct impression from the powers that be (writers, directors, actors, Gene, etc) intended for shields & screens to be the only real defense the Enterprise had. Any hit that could get through the shields meant the ship was a goner. Even from a pacing point, you'll notice how tension ramps up when the shields are about to give. Only after TWOK was the concept that the ship could take weapons fire invented, and then dramatic pacing for shieldless hits in later Trek became common place.
The Borg won't win any points for aesthetics, but as far as practicality, a windowless cube with decentralized systems is pretty hard to beat. Starfleet's ships are prettier, but tactically horrifying -- bridge full of senior officers in a see-through dome on top of the ship, anyone? Shields fail sometimes, people!
In TOS, we never really saw the Enterprise fire all her weapons, plus whenever she fought it was mostly from one angle. You tend to be forgiving of older SFX since it creates a kind of bias as to ship tactics and other things. Nobody ever attacked them from above, for example.
I mention that because while I give the TOS-E a pass, I can't do that for the E-D. Their most powerful forward weapon has a decent area of fire, but if the enemy is hovering above you (say, in a primo spot to blast the exposed bridge), your torpedo launcher is at the worst possible spot! It's blocked by one of the thickest areas of the ship, too! Ugh.
When the E-E had torpedo launchers behind the neck that could fire up, I was a bit relieved. But then schematics say there's only one quantum torpedo launcher, and it's located *surprise* below the saucer section once again. Bah!