The media will 'ignore' Rand out of legitimacy, just as they did his father even if he were to win some Primaries. Happened with his Dad, well before his self destructive statements regarding foreign policy.
I don't think that will happen for several reasons, all of which surround the issue of electability. First, Rand is a much more mainstream candidate than Ron was. Rand has libertarian leanings, but he deemphasizes the areas in which libertarianism conflicts with the GOP base such as on foreign policy and drug policy. Ron was a vocal non-interventionist. Hell, he bashed the Iraq War as hard as any Democrat. He also talked about drug legalization more than Rand does. Essentially, he focused on the areas where he had disagreement with the GOP and often said goofy things. Rand touches on some of that, but he doesn't hammer it. He emphasizes what usually appeals to GOP primary voters, making him much more philosophically viable than Ron was.
Second, Rand has a track record of winning big races, and Ron doesn't. Ron was elected to a gerrymandered Republican congressional district in Texas. He never had to run a big race. Rand ran statewide, won a contested primary, and defeated a fairly strong Democratic opponent in the general election in a state that is GOP leaning but not lopsidedly so.
Third, Rand "looks the part" and "sounds the parts" a lot more than Ron does. Even though his supporters were young, Ron is an old man and has looked like an old man for about 20 years. Furthermore, even when young, he was spooky looking. People weren't going to vote for a guy who looks like Ron Paul. He also was a mediocre speaker - frequently stumbled over his words, etc. By contrast, Rand is a decent looking guy and speaks well. He also has a hot and charismatic wife, and yes, that matters in politics.
The media ignored Ron, because they knew he was a freak show whose appeal didn't extend very far past a few pot-smoking conspiracy theorists. He wasn't a serious presidential candidate. They've paid attention to Rand as a Senator, and they'll pay attention to him as a presidential candidate.