No, the battery should be fine, it is not in the ignition light circuit. Was it a new alty or a reco, or just one out of another car? It sounds like the alty is charging OK, maybe its a wiring issue.
The charge light circuit looks like this-
or like this-
which shows both internal & external regs.
Have a read through this too-
http://wilbo666.pbworks.com/w/page/39441708/Toyota Alternators