The short answer is no.
You probably are asking because you've heard people say "long time no see" and by analogy you wanted to use a different verb. "Long time no see" is a set phrase so you can't actually change the wording.
That said, native speakers CAN say "long time no eat" as a joke because it's obviously wrong, but both of them know it's wrong and know the meaning, but as a non-native speaker if you said it, people might think you actually believe it is correct grammatically speaking. It's a strange situation where the only time you can say this is if other people know that you know that it's grammatically incorrect.