Indeed, we were never told that the ship would lack air or other life support. Instead, our heroes were unsure whether there would be a ship at their destination at all, or mere empty space.
But Spock did say the ship was "functioning" and suspected that "mutineers" would be hiding elsewhere in the ship; had there been a life support shutdown or failure, Spock would probably have referred to it at this point, if only to clarify the tactical situation vs. the mutineers.
That Kirk and pals didn't immediately remove their suits was obviously against Hollywood convention and Star Trek precedent. It made sense, though, as the ship had been observed doing the "now you see me, now you don't" act previously, and the results would be fatal on an unprotected boarding party.
As an anti-contamination measure, the suits would obviously not have worked too well, because they wouldn't stop "fabric of space" from hurting the wearers. But anti-contamination has never been attempted with suits in Star Trek anyway. Spacesuits and other protective gear seem to be worn only against "the elements": cold, hot, vacuum.
Supposedly, the crew of the Defiant
had three weeks to kill each other. They could have achieved total loss of life without having to resort to means of mass murder (opening of airlocks, toying with gravity, using intruder control gases etc.), at least if we assume that the final bouts of murderous rage would result in suicides when there were no other victims immediately available. The brain damage itself need not have been one of the causes of death, merely the driving force.