Probably not both 32 and 64 on one license, but you know, nothing better than phoning Adobe's customer service and you'll get your answer "straight from source".
Phoning Adobe is a great answer and could probably solve this many other problems.
You are always so helpful, but do we have a bad day? Don't take it out on a poor soul.
Please do keep contributing with the great knowledge you have and have shared so kindly and freely.
Despite the fact that some of it I can call Adobe about or read elsewhere.
We are all here to learn something, none of us have all the answers, but collectively we have a good deal of them.
Take care and keep smiling
PS: I very much enjoy your articles here, and I value your contribution here, thanks for sharing
PPS: for OP. CS4 when installing on a x64 windows machine will under custom install install both x32 and x64 versions of Photoshop and is counted as ONE install. Good luck :-)