Ryan, As far as we know Google "PR" or Page Rank is an algorithm developed by Larry Page way back in the day that determines web page importance by the number and type of links are pointed to it. What you have described only has to do with your pages own outbound links. The general theory is that the more outbound links on your page, the more you dilute your own PR. (Then of course there are those camps that say that PR makes no difference anyway, but that is another discussion for another thread)
What you have described doing is a form of cloaking and may in fact help your PR due to the fact that Google sees less outbound links when they come to crawl your site. However, I do not recommend this practice with a domain that is important to you. This is because of the fact that Google has stated publicly that they will ban cloaked domains. You may never get caught but you are on thin ice. If you use a throw away domain that would be the best way to test such a strategy.
Another recommendation is to not just use user agent strings to determine spiders. Why? They are incredibly easy to spoof and it will be relatively easy for Google to "break" your cloaking algorithm and find out that you are serving different pages to their spiders. Rather find yourself a good ip list, throw those into a mysql table, and use php to check to see if the ip hitting you is in that list. Volatilegx actually runs one of the best ip lists on the web. I am not allowed to give out a url here but go to Google and search for "ip lists" (without the quotes) his is the first link that shows up.