Chances are they wouldn't (if you were reasonably cautious with, e.g., your phone). But if they find out you don't later they can throw you in jail and deport you. Lying to federal officers while getting a visa over something as innocuous as a social media account really doesn't seem to be worth it under basically any circumstances.

I have no idea what they actually do, but I'm guessing they could simply search for the accounts, or ask other people you know.

I'm not sure that's true. Membership in a terrorist group is specifically mentioned on their list of ineligibilities.