- I have not heard ever about the ground plane size and the noise reduction, but that doesn't mean whether is true or not.
Edit: In the case of an antenna ground plane, if the ground plane is too short, your radiation pattern might change and the directivity might decrease. In this case, by increasing the ground plane size you will achieve a higher directivity, and therefore your received power will increase. Then, your Signal-to-Noise Ratio (SNR) will increase, and it will be seen as a reduction of the noise.
Since a GPS antenna is pointing to the sky, it is true that if you increase the ground plane size you will reduce the backlobe of the antenna, so you will be receiving less thermal radiation emitted by ground.
Note: If the "noise" is generated by other devices behind the ground plane, then you could be reducing the coupling between the antenna and that "noise" source, but formally this is not noise, it is an interference.
- About the vias, the first image shows a coplanar grounded waveguide. In b) you can see the fields propagated in it (E, electric field, and H, magnetic field). If you have other components around, there is some risk that one of these lines reaches the component, inducing some currents on it. In this way, the signal passing trough your waveguide is coupled to the component, other transmission lines, etc.
By adding these vias you are trying to contain the electric field in the dielectric below your transmission line, that is, you are trying to reduce the coupling with other elements:
This is specially important not only in amplifier chains, where you are in risk of retro-alimentation and then unwanted oscillations, or in switches, where the coupling can be higher than the switch isolation, but also in oscillators, in filters, mixers...
Or at least this is what I think...