Unfortunately, no. I suspect the issue is rendering, especially since the player database already resides in memory. The Database tab will be faster due to paging of the players. The "Add Players" dialog lists your entire database of players in a single list, and if you've got thousands of players, it can take a few seconds to render. I've streamlined it as much as I know how, and what's left is really up to IE.
I have tried, a long time ago, to save certain rendered elements from dialogs for re-use to speed things up, but it's just not possible as IE (and other browsers) treat it as a security issue (I could be wrong about the reason, but regardless you can't take an element from one window and use it in another, which is what saving a rendered element would amount to).