Of course it cares. The audio you hear out of the guitar is 100% the audio you hear for your strings. It is 100% signal based audio, and the way it emulates bodies and pickups is by putting the incoming audio processed by convolution captures of the actual pickups and bodies.
It's why they use piezos, because it's the closest thing to the sound of your strings raw without the pickups coloring the tone.
In a sense, the Variax is extremely reliant on the sound of your strings. Without the piezo pickups, it cannot make the guitar sound like a humbucker, a single coil, or any of the other nuances it needs.
I actually tried acoustic strings on the Variax once, and since it's piezo and not magnetic, it will pick up the sound. The sound ended up very different. Electrics were unusable. Acoustics actually sounded better though, because, it's acoustic strings.
I actually made an audio sample demonstrating the difference between Modeling (Variax) and MIDI (synth or sampling). A MIDI guitar is what doesn't need to know the sound of the strings, but the pitch and velocity.
First clip is the Variax, second is the same clip going into Audio-to-MIDI. Third is Variax on the left speaker, and MIDI on the right.
You will hear why the Variax is not a synth guitar, midi guitar, or anything like such.