Would Adsense let me promote my hostgator referral links? Or will I get banned doing so?

I think you're talking about Adwords

If you're talking about adworks then you can't do it, adwords will not let you promote affiliate/referral links you have to create a squeeze page to promote offers.

You talk about adwords. You can't do it directly as night owl said. But you should know that there is a lot of competition in hosting niche and the CPC price might be pretty high.

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