Not really. The factory sub is getting very little power and is mounted in an infinite baffle rear-deck application (if you have a sedan - if you have a wagon, you have a plastic ported enclosure in the rear side panel).
There aren't many woofers that work well infinite baffle, and none will work off of that amp. It's too puny.
The signal coming out of the RNS-E is actually filtered- as you increase the volume the bass is removed to keep that factory system from coming apart. When upgrading it, we insert a grounded wire into the empty "Bose pin" slot in the RNS-E connector, to force the OEM HU to stop activelly filtering the bass out at higher volumes.
You probably can't get the minor improvement you're looking for easily.
Personally, I'd rather have a 2-channel amp and a good 6 and tweeter in front, with the Bose pin stuffed, and leave the factory woofer unplugged.
Former cars include 1976 Audi 100LS, 2001 Audi allroad.
Musicar Northwest - Top 12 autosound retailer two years running!
1,147 AW posts as avincar (now at musicarnw.com)