I certainly consider hardtail Stratocasters real Strats, and I think most guitar players would agree. You may notice a slight increase in sustain and resonance with a hardtail, where a Strat with a tremolo will sound a little tighter. Overall I think the difference is minimal, but some players swear by one or the other.
Many Stratocaster players also “deck” their tremolos. This means they adjust the springs and the bridge itself to prevent it from easily moving. Another method is to “block” the tremolo. Here a wooden block is installed in the spring cavity, again preventing the tremolo from moving. Both of these methods, to some extent, can turn a Strat with a tremolo into a hardtail.
Some players feel that a blocked or decked tremolo results in better tuning stability, as well as the aforementioned improved sustain and resonance. If you intend to try it and aren’t experienced with guitar setup and repair you’ll want to leave this job to a guitar tech.
However, even if you block the trem you’ll still have a big cavity and lots of metal in the body of the guitar, instead of the solid wood body you’d get with a true hardtail. That, I think, is the root of any sound difference. Again, I think it’s minimal, but I suggest you try out both types of Stratocasters and decide for yourself.