Assuming my captain has 9 ranks of Particle Generators and stacked the consoles for it, is this possible? If so, does it work for all levels of TBR, or only let's say TBR3?

Normal torpedoes, no. But any rank of TBR can destroy high yield plasma and normal/high yield tricobalt. Also mines.

Oh and I Tried this out.

If you hit a ship with TBR and Normal Tractor beam it doesn't rip the ship in half

Mines, Tricobalts, and heavy plasma torps are destroyed.

Yeah, I was a little sad when that didn't happen... didn't really expect it to, still would have been wonderful to be able to rip ships into pieces.

Ah, thank you! I finally have something proper to slot into the Sci Lt slot that capitalizes on my generators.

TBR and TB have a shared 15s cooldown... You cannot use them together when on your own.

I'd agree that when 2 sci ships combo this could be an outcome. However, that means a 1-shot for all STF mobs, and you know Cryptic would never allow that.

Actually, a Repulsor + Tractor Beam combo would be virtually useless in achieving this. The push of the Repulsor would be negated by the pull of the tractor if the ships are on the same side. (The same problem a single ship would have if it were not for the cooldown issue.) If the ships were, say, at a right angle, you would simply change the direction of the push. Even worse, if they were on opposite sides, the push + the pull would combine to shove the targeted ship through the one doing the tractor.

To achieve the destruction of a ship using these powers, you would need ships on opposite sides of the target doing the same power. Two tractors would pull it apart. Two repulsors would crush it. That is, if those powers worked that way.

Form a triad with two fellow sci officers
Tractor lock the same ship
Its shields will fail and its hull will break in a matter of about 30 seconds