I highly recommend skipping on the HC carpet without CO2. It's really hard for HC be successful without it. I'm dong it at work in my office nano tank, and it's been a struggle. I started off emmersed and got a really nice carpet going. Since flooding it, I've struggled with algae issues and with keeping the HC healthy. It's still going, but I wouldn't ever attempt it again without CO2.
It started looking like this:
This is how the HC looks just less than 3 months later, and I dose Excel, micros, and macros every single day.
So yes, it's alive and all, but I have never had to trim it once (so it's not really
growing), and it's much more thin than when I started. You can certainly have HC in your tank without CO2, I just think it's super hard to maintain an actual "carpet" without CO2.
I am probably going to start this whole tank over, because I don't really care for how it looks anymore.