You can also get pressure signs from a 223 in a 5.56...
They're the same case dimensions. The difference is how any one round is set-up. IE: Bullet, charge, OAL, etc. ALL of this needs to be considered when looking at a load to shoot in your rifle.
The 223 Rem and 5.56X45 NATO are the same round. 5.56 marked chambers are typically set-up to shoot the longer steel-core FMJ military rounds, so they have a touch longer leade. If you have a short cut 223 chamber and stick a long 5.56 load into the lands, you could see pressure. But, fundamentally, they’re the same.
The only way to answer this is you need to shoot your intended load and evaluate for signs of high pressures. There is no universal 223/5.56 chamber dimension, literally dozens of different reamer specs exist.
IIRc, the S&W is set-up with a touch longer leade to accommodate any and all factory loads. But only shooting and evaluating the brass and such will be definitive.