in premiere, no i don't think there's another way. i'm not a premiere master or anything, but from what i remember, it doesn't work like that.
but, if you were in a music editing program, it definitely would.
there's a program called Magix Music Maker 11 (i'm using version 7, actually). Super cheap, like $60, and you can get it at Target (or anywhere any kind of games or software is sold). It's awesome. I've played with Acid, a tiny bit with ProTools, lots with Audition... Magix is the best. it can do anything Acid and Protools can, and it's super easy to learn to use. I use it for sound design and editing for my short movies. it allows you to bring in a video and sync up perfectly with it. I've had so much fun in it, I've even done a few songs and a couple radio dramas as well.
my normal workflow is to work in premiere or after effects, build temp sound in those programs, then when the video is close to being a final edit, i render out a lowres version to bring into Magix to really do the sound right. then i "render" the sound as a single WAV and bring it back into my editing program and turn off or delete all the temp sound stuff. then, when you render your final hi-res video, your perfect sound will be in there.
i'm gonna get slammed for saying it's better than protools, but, whatever.
also, i do still use Audition. Magix doesn't include a noise reducer (a good one, anyway) with Music Maker, although they do offer one as a stand alone program. So i use Audition for noise reduction.