Hi Sandy,
While only your own ears can tell you if the result is an improvement, I think the chances of you having success with a USB DAC vs the analog mini jack are pretty high. Computer internals are often very noisy environments and most computer manufacturers aren't placing a high priority on the isolation of the soundcard from other components which can introduce signal noise. In addition, the quality of the D/A conversion may not be great because most PC maunfacturers are also outfitting their machines with cheap audio circuitry.
If you're willing to dive into the details, my suggestion would be to spend a bit of time on a site that specializes in computer audio playback. My personal favorite is one called Computer Audiophile. In addition to equipment and software reviews, they have a very active forum, with one of the most active sub-forums being the one covering DACs. Here are links to both:
http://www.computeraudiophile.com/
http://www.computeraudiophile.com/Forums/Equipment/DAC-Digital-Analog-Conversion
A word of warning here though is that this category of discusison is a wormhole that can suck you in way beyond where you ever intended to go at first. So, if you find yourself spending hours digging through, don't say I didn't warn you! 
As to your mention of HRT, they do a very good job and have been establishing themselves as a serious player in this space. That being said, there are tons of options out there with more coming out each month. The DAC space has seen a huge revitalization in the last few years and many companies are focusing on computer DACs given the trend towards computers as audio sources.
Jeff