Gifted money from overseas but gifter wants to remain anonymous. Money will come into a US account. Is this even possible

Yes, no problem.

If the gift amount is LESS than $17,000, you do not even have to submit any reports/returns.

Money laundering?
Scam?
From a corporation? (Threshold for reporting on 3520 is $15,601)
Not a gift in substance?
Not sure where the $17,000 number that ATE mentions comes from?

Traveling, so I cannot research the gift tax exemption amount, but I thought it went up to $17K.

I will yield to IntlTax on the Form 3520 threshold.