I would disagree with Chadnliz. Having run my full-range speakers with HT and also with a Sub, the sound is much better with a sub. There are numerous threads here that argue back and forth as to the best way to integrate a subwoofer. My personal experience (and a lot has to do with room dynamics, speaker placement and listening position), the sub crossed over at 80 hz worked better than 2 full-range speakers that go down to 22 hz.
Also the LFE is not a dedicated discrete channel (hence the .1 designation). The LFE will contain deep music as well, the amount of which may depend on the cross over setting. Since you don't have bass management, I'd probably run my main speakers through the cross over in the sub. In this way, you allow the sub's high-pass filter to act as bass management for your mains. Otherwise, you will duplicating the LFE effects (full range speakers PLUS the sub), which will probably be overkill.
Also the LFE is not a dedicated discrete channel (hence the .1 designation). The LFE will contain deep music as well, the amount of which may depend on the cross over setting. Since you don't have bass management, I'd probably run my main speakers through the cross over in the sub. In this way, you allow the sub's high-pass filter to act as bass management for your mains. Otherwise, you will duplicating the LFE effects (full range speakers PLUS the sub), which will probably be overkill.