The Dude has a power transformer, but is not transformer coupled. To answer the posters question, yes the transformer can and does certainly influence the sound of a preamp. Depending on the design of the preamp transformers can be used in several locations. They can and must used in the power supply, can be used as chokes in the power supply and some use them for coupling.
In each instance the transformer can and does impact the sound regardless of use or location.
In each instance the transformer can and does impact the sound regardless of use or location.