Not quite. One would assume the good people of the USA would be able to choose their candidate based on their perception of her ability to serve the people. The royal connection only gets her extra visibility at the outset, the rest is up to her.
I tend not to voice political opinions on TRF, as it is against the rules, and more importantly, can sidetrack the conversation very quickly.
However, the reason I support her running for public office in the US, if that is indeed what she wants to do, is it will allow her legitimately obtain a public position. So far, her public profile is based largely on her relationship with Harry. In football parlance, that is a "WAG". She has been vocal about using her "voice", and running and getting elected to public office in the US will allow her to not just use her voice, but also achieve something for the greater good that she seems to be keen to pursue.