Wow! This is a mouthful! Let's take the last first
<<How's the accuracy, generally?>> I use it as a base bullet for load development. Maybe because I'm convinced of its accuracy.
<<Is there a downside to this bullet?>> Uh, other than cost, not that I can think of. And they're not that expensive unless you shoot a lot.
<<...a 7mm-08 Model 7... (I shoot this rifle a lot; I am shooting out this finicky damn barrel so I can rebarrel the rifle some day in good conscience <g>

.>> Got one of those also, finicky isn't the word for them! Very disappointing accuracy wise, but I'm still playing with it.
<<What is the common wisdom as to what the bullet DOES on impact?>>
Well, I don't know about the 'common wisdom,' But I can relate my limited experience.

I started using BT's for load development to assess the potential accuracy of the instant rifle because I was convinced it was an accurate projectile. Never been disappointed in that score. Naturally, this usually meant I had pretty good BT loads worked up when deer season rolled around. I had some of your concerns, so I started trying them out. Since our limit is 8 deer per year, I have had ample opportunity to see how they perform.
<<Will a 7mm, 140-150 grain BT at, say, 2600-2800 fps muzzle velocity fully penetrate a deer broadside?>>
In my experience with other calibers using bullets of like sectional density, yes
<<How about angled shots?>>
In my experience, up to about 30 degrees, yes
Examples this year are 2 average sized Georgia bucks, both shot behind the shoulder on the near side, the BT angling forward to exit through the far side shoulder blade. One with a 300 Win Mag loaded to 30/06 velocity (an honest 2940 fps, not the 2920 claimed by the factory), the other a 180 gr. 338/06 at a little over 2700 fps as I remember. Range on both was about 40 yards, both dropped instantly, 50 cent piece entrance and silver dollar sized exit.
<<Lengthwise?>>
Dunno, only shot lengthwise on a deer (from front) one time and that was with a
would assume, in that caliber, velocity and sectional density, anyway, that the BT would not either.
In my opinion, the Nosler BT holds together better then Hornady Inter-lock bullets and has become my favorite projectile for deer in calibers 6.5 mm and over.
Richard
Richard N. Elliott. Former Captain of Horse & Keeper of the Peace, current Interpreter of Statute