Wirelessly posted (8700g: BlackBerry8700/4.2.1 Profile/MIDP-2.0 Configuration/CLDC-1.1 VendorID/100)
alstang1, see http://blackberryfaq.com/index.php/M..._on_BlackBerry
for background info, if you haven't already.
I use the BIS to have my @tmo.blackberry.net email as well as my yahoo email and email from two personal ISP accounts delivered to my blackberry. I do not use redirector. For what it's worth, I think most recommend against redirector because it is flakey.
But regardless, the blackberry does not sync with the email client on the desktop computer, at least as far as I know, and according to everything I read here on BBF with the exception of dbaci3 above.
If you get interested in switching from redirector, see the blackberryfaq articles on BIS.