Apple Remote Desktop 3.0 was released in 2006. The current version is 3.6.1, and as such your six year old boxed copy license still entitles you to run it.
ARD has undergone some major changes during that time: most notably, Apple switched it from a Postgres database to an SQLite database, which greatly reduced its memory footprint and made it much more self-contained.
After reinstalling Mac OS X on my computer, I didn’t want to first install my boxed copy (version 3.2) because I didn’t want it to bloat my system with a copy of Postgresql that would get replaced by the update anyway.
After six years, it’s a safe bet that the downloadable Admin Update 3.6.1 does not require any previous version’s files. However, the installer checks for the existence of a previous version before allowing you to select the destination drive. This check can be satisfied by first running
defaults write /Applications/Remote\ Desktop.app/Contents/Info CFBundleShortVersionString -float 3.0
I’d like to point out that it still requires the license key that came in the box when you first run ARD.