I loaded a bunch of Missouri Bullet 125 grain RNL .356 bullets as .38 Special plinkers here recently. I didn't have any leading problems and accuracy was not bad at all (of course I wasn't shooting bullseye targets, so YMMV).
The only real problem I had was that some brands of brass (especially R-P) don't grip the bullets well since they are undersized, and they lack a crimp groove, so I was basically creating my own with a Lee FCD. I saw OAL flux due to this issue, but with my low pressure plinkers it wasn't that much of an issue.
Its not ideal. I did it because I had a bunch of the bullets and I decided to stick with heavier bullets in 9x19mm and I didn't want to waste the 125 grain RNLs (or load them in 9x19). Once the .356 bullets are gone I'll get .358 125 grain bullets for my plinkers.
Now I'm working in the other direction, loading 158 grain .358 RNL bullets in 9x19mm. So far I've had good luck, no over pressure signs, no excessive leading, and good accuracy.