The grapes would alter the flavor profile, depending upon how many grapes you use, the kit and the grape variety. It might be better to try the kit as is and use the grapes in conjunction with a country style wine like blackberry - especially given the fact that you don't know which varieties you have. Raisins are good, safe additions to wine kits.
With fresh grapes, you'd want to crush them and add the proper amount of potassium metabisulfite to fix, or set, the color and to kill any unwanted wild yeasts. Another thing to consider when using fresh grapes is the possibility of a secondary, or malolactic, fermentation which would be detrimental to a kit.