So I just wanted to give an update here for anyone who stumbles upon this thread possibly asking the same questions.
I have a buddy of mine who has a nice computer speaker system. A 2.1 setup similar to the one I linked, but slightly better quality.
I went over to his place to test out the sound quality of running my bass through his PC using Amplitube and coming out the speakers.
While the sound quality is better than the speakers I've been using, I did notice where it started to fall flat.
On the low notes, like an open E string, the frequency was there, but the volume wasn't. The speaker hit the note, just not very loud as compared to me hitting an A note on that same E string. That A note was way louder. So when your playing to music, the volume is inconsistent because the speakers appear to only play certain notes at certain volumes. It's still doable, but it's hard to match your music volume to your bass when your trying to focus on what you are playing.
With that being said, I did pick up a Fender Rumble 25, and it is quite different than the PC speakers (Obviously). The music coming through the Aux input on the amp isn't as good as I'd like. (Through headphones it's great) But I split the difference and got that 2.1 speaker setup, along with the amp. Now if I want to jam out with some volume, the music goes through my 2.1 system, and my bass goes through the amp. The quality is fantastic.
Trying to run Amplitube out my PC to the Aux input on the amp didn't really give the quality I was looking for however it may be better if I tweak the settings a bit on Amplitube, I just haven't gotten around to it.
Regardless, I have a setup now that works great. Again I appreciate the feedback you guys provided me, and in the end you were right. Nothing substitutes a good bass amp.