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The built-in amp (50W?) for your proposed sub seems rather small, and should not cause a problem. The drain on your electrical system from such an amp is trivial compared with what your air conditioner uses. I have a 550 watt amp in my HCHII, and the only time I notice battery drain is with the AC blasting in city traffic. My system is puny compared with what some people install.
If your new subwoofer starts rattling every panel in the car, and you get annoyed, and you take your car apart to add hundreds of pounds of deadening material, well, don't say I didn't warn you: your fuel economy will suffer in proportion to the weight added.
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