Yes, these will be a very noticeable upgrade. I've never heard a pair of Logitech speakers that I've liked, including the Z 5500 (although I haven't heard some of their newer models, not that I expect much). It looks like yours don't even have tweeters, so that alone is a big place to improve. Just make sure to grab some stands at the same time so that you can position the speakers properly and isolate them from your desk. You want your tweeters at ear level (or close enough to tilt the speakers to make up the difference), and you don't want the vibrations of your loudspeaker cabinets transferring into your furniture, as this muddies up the sound.
I would recommend a pair of IsoAcoustics ISO-L8R155's, as they provide excellent isolation and adjustments, but if that's a bit more than you want to spend on stands, AudioEngine's DS2's will work also.