Do vias introduce more noise to signal
A via doesn't add noise, per se, but it does represent an opportunity for noise to be coupled to your signal that is different from the opportunity along the traces.

Noise couples to your signal through capacitive coupling and inductive coupling. Both will happen along a trace and along a via of any length. How much depends on the aggressor signal, geometries and materials.

NB: As to the other answer indicating that vias create impedance change for high speed digital circuits: This is not really the problem. If you have different trace impedance on different layers, then obviously you will have a reflection from switching layers. Vias can be used in high speed digital circuits to above 25 GBps as described in my blog here.