Your dealer is kind of wrong. That goofy little Rel sub won't get you that much deeper extension compared to your speakers, but it could help to smooth out the low-frequency response of your room. The problem is that your integrated amp has absolutely no EQ abilities to help that, and it doesn't even have rudimentary bass management as far as I can see. It simply isn't built for adding subwoofers.
To be honest, I wouldn't add a subwoofer without some kind of bass management. Otherwise, all you will be doing is boosting bass levels. If all you want is louder bass, sure, add a sub, but you won't have much of a way to integrate it properly.
For a system like yours, I would be looking at
this analog Hsu high-end crossover to integrate bass management into your system. Then add a sub that doesn't use DSP in the signal path. Hsu and Rythmik use analog amps. I think the Outlaw Audio Ultra-X12 also uses an analog amp. The reason you should be looking at analog amps is DSPs add latency that you have no way of compensating for in your system. Rel uses analog amps, but they have pretty sad performance for the money, their decent subs cost a fortune. I think Starke Sound uses Analog amplifiers but I am not certain.