No he can't. You can only download past purchases (including auto-download and Match) for one Apple ID *per computer* (not per account), and this can only change once every 90 days.
This is the incredibly annoying distinction between "authorization" and "association". You can "authorize" content for several users on one machine, but in order to re-download content, you have to "associate" a computer to that ID, in addition to authorizing it, and this can only change once every 90 days. Having separate accounts on the computer doesn't change this.
I recently learned this the hard way when my son came home from college and re-download one TV show from his AppleID on his account. When I later tried to use Match on my account, I was informed it would be 90 days before I could switch the computer back to my ID (and no, going to the site and removing it from the authorized list won't change this).
Luckily, I emailed the iTunes store, and they reset it, but made it clear this was an exception to the rule:
http://support.apple.com/kb/HT4627
This is such an annoying and confusing policy, that hopefully Apple will change it soon- especially with enough negative feedback.