Yes.
As you said yourself, the HTS-100 is a starter kit. It's designed to get people up and running and give them something better than they'd get from a typical Blu-ray-drive-based home cinema system that you might find in a Comet store. If we look at the specs, the main surround speakers use a single driver in each to keep costs down, but unlike a BMR driver, these weren't designed as a hybrid tweeter/midrange driver; they're being asked to do something that's a bit of a stretch. IIRC, the sub is passive too, but I'm not 100% sure on that. If it is, then that's another cost saving compromise. Powered subs are more expensive to build, but they work better.
Putting all this in context, someone with a HTP100 kit might reasonably expect to upgrade the speakers at some point, and make the move to one of the packages with a powered sub and better satellites. That in itself would be a big upgrade in sound, unless of course the room is a complete sonic disaster which makes it impossible the really hear any change. A decent first step would be something along the lines of Wharfedale or the CA Min12 + SX120 sub at around £350-£400 for example. You're planning on leapfrogging that step and going all in with the £650 Minx 22 kit, so yes, it will be a noticeable jump in performance compared to the speakers from the HTS-100 kit.