Poisson's ratio does not represent compressiblity of soil. The soil compressibility is expressed as function of compression index, swelling index, coefficient of volume change or coefficient of consolidation. These parameters depend on the applied pressure, initial void ratio and soil permeability
Yes, the compressibility characteristics of soil can be influenced by Poisson's ratio..for example many people derived the coefficient of volume compressibility in terms of elastic properties such as Young's modulus and Poisson's ratio..The settlement due to consolidation (compressibility) can be calculated using coefficient of volume compressibility..find attached herewith some article relevant to your question..ok all the best..
Yes, the situation is quite complex as the compressibility is influenced by many factors, of course those include the Poisson ratio of the elastic phase but there are many other factors involved. Here's another nice reference: