Can I run full-wattage T12s on newer electronic T8 ballasts?

I'm sure there is a label up in the fixture that says only to use 32w T8s but I can't see.

I'd like to put F40T12N (Natural White) tubes in the three-lamp troffers in my office.

Any advice?

You can, but they'll run at about 60% output like running on low-output shop light.  Lamp life might be lower for running dimmed at 60% power with no cathode heater power at all.

Instant starting won't help electrodes either. 

I've ran both standard F40T12's and the 34w 'energy saver' version plenty of times on F32T8 ballasts and never had a problem. (but as Luminaire mentioned they will be dimmer than normal)

A light I put up in my kitchen came with a pair of electronic instant start ballasts.  On the fixture box and instructions, it said it could run F40T12 or F32T8.  The ballast labels listed almost every medium bi-pin out there as being able to be run on them.  I used F40KBs because the store had 4 of them at the time.  The lamps burned out after a month from heavy sputtering from operating in cold cathode mode.  I ended up replacing the ballasts with a pair of Valmont HPF magnetic rapid start ballasts and a new set of F40KB lamps.  After 7 months of use they didn't even have any rings formed yet 

I have a a striplight that I put up in my utility room that came with a no name electronic rapid start ballast that said it could run F32T8 or F40/34T12s. I'm currently running T8s in it right now butI wonder if the lectronic rapid start F32T8 ballast will run the F40 better than the IS ballasts since the cathodes should be heated like the F40 ballasts.

Only ghetto ballasts will endorse that.  There are many ballasts that do not even meet ANSI specs. 

On a 2-4' rated ballasts, an F40T12 will run at about 80% the power of F32T8 based on my measurements. Since the ballast is constant current and lamp determines the voltage, 25.6W would mean that to the ballast, it's just like driving a F25T8, or F32T8/25W. 

Ballast spec includes supported lamps, and ballast factor rating. 

A common T8 normal ballast has a BF of 0.87, which means that when a lamp is operated on that ballast, the lamp's output will be 87% of catalog spec. 

A normal magnetic ballast usually is rated 0.95.

What these F40T12/F32T8 compatible ballasts don't tell you is the difference in ballast factor. 

F40T12 will run at 80% of F32T8.  Since the F32T8 is already driven at 87% of spec, this means that F40T12 can be estimated to produce rated 87% on T8 * 80% of T8  * 32W/40W = 56%

You can get T12s to run at close to 70% output if you use a 1.20 BF high-light ballast (not to be confused with "high output" which is designed for a different system).

If you use a Sylvania PSH high-light T8 ballast(which is rated for F17 to F32 and F40T12 is similar to F25T8 once running)  with T12 lamps, you should get an acceptably good (70% of rated lamp spec) output and good life.