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I have an '02 S with the Bose system (6 channel amp, dash & door speakers, plus optional rear deck sub box). My Becker took a crap so I replaced it with a JVC CD/HD Radio head unit from Crutchfield and installed it myself along with new dash speakers. The h/u installation was fairly straightforward and is a vast improvement over the Becker.
Since I really didn't dig into the amplification end of my system I can't give you a definitive response to your question. However, the sub is generally going to be the most demanding part of a system in terms of required amplification. The dinky amp in any head unit won't even come close to providing the power necessary to properly drive a sub, and I doubt very seriously that was the case with the factory head unit.
From the Kenwood you're going to take preamp outputs and connect them with the Metra harness to the factory harness, which feeds the factory 4 channel amp powering your dash and door speakers. If there's a way to connect the factory sub, I'm almost certain it will be integrated into the 4 channel amp.
On my car there's a flat plastic connector for the sub on the right side behind the passenger seat up next to the deck where the sub mounts. To really get a good look in the area you'll need to put your soft top into the service position, like you're going to access the top of the engine. You may have to dig around, but it's probably there. If you can't find it or aren't clear where to look, I may be able to upload a photo of mine.
If you don't have the factory connection you may need a dedicated amp to drive the sub. The sub was a fairly common option. With your upgraded factory system I have a hard time believing the plug isn't there.
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