If I use thicker underlay under my floor, will it feel softer under my feet?

Thicker doesn't necessarily mean softer under feet.  Underpad is measured in weight per cubic foot of material.  The more support you give to the carpet the better it will perform.  A heavier underpad will give a firmer more luxurious feel, making the carpet feel thicker where a lighter weight cushion may give a softer feel but not provide as much support.  It is often said the better the underlay the better the performance you get from the carpet.  In fact many manufacturers will increase the wear performance and better warranty base on a better underpad.