Is surname Judah/Juddah Jewish?

There are really no "Jewish surnames". That is, most surnames that are carried by Jews are not exclusively Jewish, but can be had by people without any Jewish connection whatsoever. Some surnames are more common with Jews, but absent any other information, you cannot assume the bearer was Jewish.

So, Judah sounds like it could be biblical in origin, but biblical names are popular with Christians too, especially in some eras.

Also, spelling is a 20th century invention. It was not necessarily stable before. Furthermore, most Jews did not use the Roman alphabet in those days (having Yiddish, Judeospanish or Judeoarabic as vernacular and living in Russia or the Ottoman empire), so there would likely have been a step of transliteration on arriving in America that would have been somewhat unpredictable.

Oh. And Jews didn't really have surnames until the authorities forced it upon them which happened somewhere 1800-1830 depending on area. You don't write when your gggf came, but if he came in the early 1800:s the last name that he used could simply be his patronymic.

TL;DR You need more information to be able to tell.

To provide an answer here I am going to use quotes from two comments on your question.

From @Gary:

There's a great book by Dan Rottenberg called "Finding Our Fathers-A Guidebook to Jewish Genealogy" that will help get you started. There's a list of surnames in the back - a couple of thousand - and for JUDAH it says there's a family in Newport, RI going back to the 1600's, a Russian family fm Grodno going back to the 1500's, also families fm Jamaica and Surinam. It says the American family is related to the Hilbert, Seikas, Hendricks, Jonas, Hart, Levy, Correa and Hays families. Also, the Russian Judahs are related to the Ioudich and Danovich families.

and from @mevaqesh:

according to http://en.wikipedia.org/wiki/Judah_%28surname%29 "Judah is a Jewish surname".