So I have a page that I don't want to appear in Google Search Results, however on that page are links that I DO want Google to follow. So my question is will Google find those links.
So instead of using robots.txt to disallow it, you should use the robots meta tag: <meta name="robots" content="noindex, follow"/> HTML: This will do what you want.
You should use HTML <META> tag to tell robots not to index the page, and Google scan it for links to follow. For example: <head> <META NAME="ROBOTS" CONTENT="NOINDEX, FOLLOW"> </head>