I've had a school of about 40 cardinal tetras in my planted tank for the last 6 months or so. They are doing wonderfully and are as bright as can be. My GH is about 22dGH and my pH is kept at about 7.0. Temperature is usually about 76-78F. Based on my experience, I'm sure you will have no problems keeping them with your water parameters. Apparently, much like discus, they only need the lower parameters for breeding purposes.
The only thing to watch out for with cardinals is that most of the time they are wild caught and thus are very stressed and/or starving by the time they get to you. Be sure to quarantine them, as they can be sensitive at first and many people lose cardinals when they first get em. (They get sick easily at first, probably due to stress of the change from wild to tank life.) Once they're settled in however, they are very hardy.