Yes it is possible. As Brandon1 mentioned some headunits do beging to limit bass to prevent distortion. But not all of them do this, I dont know much about infinity's stock radios so I can't tell you for sure. Even if the HU does beging to limit bass at higher volumes you should still be good to go at reasonable listening levels.
Now depending what kicker amp you have, will depend what products you may or may not need. If the amp has speaker level inputs (not all of them do) then you dont need anything special to hook it up to you car. Tap the rear speakers for the speaker level signal and then run it to the amp (as well as the rear speakers still). That would provide the amp signal for the sub.
Now if your amp does not have speaker level inputs you will need something along the lines of a Line Output Converter. May companies make then, heck I think even walmart sells them. They are a simple tap into the rear speaker wires, sometimes a power, ground, and then run the RCA's to the amp. They can be purchased almost anywhere. I might suggest crutchfield.com . Yes I know they have slightly higher prices but their customer support is top notch and they are awsome at working with you through wiring issues or any questions you have during the install. And their hours for customer support are even better (8am to midnight est. 7 days a week)
The issue I have with something along the lines of what Brandon1 stated (which is not a bad product at all) but if you are going to spend 150 for that why not get a cheaper aftermarket headunit and avoid the need for it all together.
Adverse effects, not really. Obviously it wont be aftermarket quality but you seem to know that. While it may not be aftermarket it is still going to be better than a subless stock system.
I hope that helps a little.