A properly regulated linear power supply could improve the sound, it shouldn't degrade it at least, but the question is whether you think the current level of sound from your Squeezebox is deficient enough to spend another £150 trying to improve it. Are you using the analogue or digital outputs from the Squeezebox? The power supply might make the analogue output sound better but not so sure that the digital output will improve measurably.
I had a quick look at the power supply you mention, and there are plenty of positive reviews which may help you decide. What seems to be missing however are any specs e.g. stability, regulation, ripple and noise etc. If these were available then you might be able to compare with other power supplies (from cheap £20 supplies upwards) to help you make a buying choice.