Can a SWAT tank actually drive through a building?

To the best of my knowledge no SWAT force possesses a tank (In fact, MBTs are simply too heavy for civilian roads - not to mention bridges, etc). There are several SWATs that utilize APCs (Armored Personnel Carriers), which are tracked vehicles. A battering ram can be mounted on an APC, or even on an armored truck (link below to an armored truck using a ram to breach a door in Australia). Alternatively if you've ever seen Marvel's Thor, the opening scene of that movie involves a Hydra vehicle with a mounted ram based on the real world WW2 era Wehrmacht SPG (Self Propelled Gun) StuGIII. That'd be how you'd breach a building, not driving into it.

As for an actual tank, oh hell yes, one could punch right through a house or other unreinforced civilian structure with very little effort. There's a fairly often used bit of WW2 footage of a German tank (IIRC it's a Pz Mk IV, but might have been a Tiger) popping through a farmhouse, knocks out the entire wall. I'll see if I can't dig it up somewhere and post it. And that's a very old tank. A modern MBT like an M1A1 likely wouldn't even slow down much, unless it hit some sort of load bearing support.

yes