Mouth calls and any call that you blow (such as a diaphragm, trumpet, tube calls, etc.) will sound different with any plugs in. Being a duck hunter, I had to get used to calling with plugs in, and I was able to adapt fairly quickly.
I have not noticed a difference in friction calls, outside of hearing the imperfections a bit better.
With or without hearing protection (Tetra's) in, if you really want to hear how your calls sound, record them and listen. Recording my own calling has improved my diaphragm calling considerably. I was initially very disappointed in what in my head sounded great, but on recording was "sup-par."
In the field, you will hear birds gobble at much further distances, and hear a lot more sounds of the woods, including chirping and clucks of turkeys. I feel that the Tetra's are a HUGE asset in the field.