ok, that kinda large rather whitish connect dialog window is modal and because it is 'modal' it takes over completely and you can't do nada until it connects, as you have found.
connecting with the RA control strip mod is a non-modal way of connecting and therefore you can be doing things during the connection. this is the way i connect to my ISP, non-modally using RA strip mod.
you could do a small hack with ResEdit to make the modal connection a non-modal connection when you launch an Internet app and i think there's a posted hack for this at resexcellence.com
short of that, i don't think you can get precisely what you want.