Is synesthesia tied to experience? For example, do color blind people only able to perceive experienced colors through synesthesia? E.g. if a person both has synesthesia (like grapheme-color synesthesia or chromesthesia) and some kind of color blindness (say, protanopia, when individual can't experience "red" color) will all his/her synesthetic experiences be tied to the colors experienced? Or can synesthesia make a person feel "new" color (or any other experience)?
Can synesthesia make a person feel "new" color (or any other experience)?

The answer may be yes. You can find this quote “V. S. Ramachandran and E. M. Hubbard (in their 2001 PRSL paper) described a partially colorblind man with letter-color synesthesia who said that when synesthetically stimulated, he saw colors he had never seen with his eyes—he called these “Martian colors.” Ramachandran and Hubbard subsequently found that “the Martian color effect” might occur in noncolorblind synesthetes as well.” from several websites, such as this site and this site.

But I can’t find the original paper of V. S. Ramachandran and E. M. Hubbard. So, it’s impossible to verify the finding. Also, I can’t find any other reports of such a patient in the literature or any report of non-colorblind synesthetes who experienced “the Martian color effect” either. So, personally, I think this finding and the speculation that “the Martian color effect” might occur in non-colorblind synesthetes as well needs more confirmation. 

Anyway, is there evidence that a person who is color-blind since birth can experience a color that he/she has never experienced before? Will his/her cortical color perception areas, which have never generated the missing color perception, able to generate it when given appropriate stimuli, such as from the eyes after gene therapy that restores the missing cone function in the retina? The answer from animal experiments is yes (for example see Ref1 and Ref2). So, potentially, a colorblind brain can still generate a color percept that it has never generated before, when given appropriate stimuli. Theoretically, then, synesthesia may be able to make a person feel “new” color he/she has never felt before if it can deliver appropriate stimuli to the color perception areas.