I grew this way for a long time, actually. It was a small utility room on the outside of my house at the time, where the washing machine was. There was no intake and no exhaust, and I never bothered to generate co2. Much like you I was concerned about this when I knew it was going to be my only option, but I went through the motions anyway, and I’m glad I did. Because everyone who told me it wouldn’t work was wrong.
As long as it’s not hermetically sealed, outside air will get in. You don’t have to worry about it. Would the garden do better with supplemental co2? Absolutely, unquestionably. But I was getting fantastic harvests, so I didn’t care that there was a way to get even better harvests. I had a 8000k btu window AC unit to combat the heat from the 1400 watts of lighting, and it worked beautifully. I had two tents in there, each with their own carbon filter and fan, so technically the room the tents were in acted like a lung room. I’m pretty sure that helped to create micro climates in the tents, but I don’t know if that would have been necessary. I used tents because each garden had its own schedule and one was sometimes in vegetative while the other was flowering, so I needed the tents for light-proofing.
Anyway, yes it can be done, without tapping into any sewage lines or anything nasty like that. Do it.