Unless you're talking about dense pack cellulose, that is not true. It's not as bad as fiberglass, but it doesn't act as an air barrier.+1 on Highbeam's comments.
I had an estimate to add to the existing 12" shredded fiberglass insulation, over-blowing with cellulose to reach R-45 which was less then $900 for 1200 s.f.. I haven't yet proceeded only because I have a little more work to complete in the attic prior to pulling the trigger.
Also, cellulose has been shown to act as an infiltration (air) barrier, so air sealing isn't necessary. However, I will likely crawl through and use fire rated spray foam to seal wiring and piping penetrations myself, but I'm sort of a belt and suspenders person anyhow.
Lastly, cellulose is treated with a borate salt, and doesn't support a flame, so fire proofing is unnecessary.
I will recommend air sealing/insulating the floor joists with spray foam. Perfect application.
Cheers!