Tholian environment ~200' C. = ~392' F. A compromised suit would expose the wearer to literally the temperatures of an oven, not to mention whatever gas may be in the environment (which from what we've seen so far, looks like their gases may be in some state of ignition). Even if the suit manages to provide some sort of magic techno sealant, the exposed area in that instant would be severely burnt, and depending on the method of seal, the rest of the extremity would be rendered useless and cauterized. If this was Sulu's arm, he'd be in need of an artificial replacement limb ala Luke at the end of Empire Strikes Back.
Although Breen use environmental suits, I don't think their native environments are quite to the same extreme as Tholians. While they may suffer from a form of heat exhaustion if exposed to our environments, that's not the same as being cooked alive if we're exposed to Tholian environments.
The temperature isn't the sole factor that determines how bad the burn is. It's also the method that the heat was transferred.
If you were to touch a piece of metal that was 400 degrees Fahrenheit, then yes, you would get a third degree burn. But, have you ever put your hand inside an oven that was turned to 400 degrees? Sure, it's hot, but your arm didn't melt off. In fact, so long as you didn't touch the metal and only the air inside the oven, you were just fine. If you would've left your arm in there, eventually it would have been cooked thoroughly, but over the short term it did no damage.
This is because gases don't transfer heat nearly as quickly as solids. So, yeah, Sulu could get a cut in his suit and so long as it was sealed within a relatively quick time, he wouldn't be harmed. And, even if he did get burned, it would likely be confined to the area of the broken seal.
Some soft-canon sources do posit that the Breen's environmental needs are relatively exotic. Given the fact that Kira and Dukat subdued Breen guards and took their suits (assuming they didn't go through all the trouble of shooting them just to find the spare suit locker), and that Worf later says no one knows what Breen look like under their suits, some suggest that Breen can't hold their form at room temperatures. Perhaps their cryogenic bodies sublimate when exposed to our temperatures. Try to unsuit them, and they're just a bunch of steaming goo by the time you get the helmet off.
That said, it could be theoretically easier for a Tholian to heat up the surrounding air than for a Breen to thermally isolate themselves in a refrigeration suit. Sure, it'd take a bunch of energy, but with personal shield generators and all, that's a definite possibility. Some comics, though, have the Tholians using another species for their ground troops in M-class environments.