No, eated isn't standard English. The past tense is ate: I ate lunch at noon yesterday.
With have, had, or has, use eaten: She has already eaten her breakfast. And when you're talking about something that happened on its own, with no helper verb, use ate: I ate lunch at noon yesterday.
Situational usage
Talking about something finished at a named time? Use ate with no helper verb: Who ate all the cake? or We ate dinner by six. Your sentence signals a completed past action on its own.
Pairing the verb with have, had, or has? Switch to eaten: I haven't eaten since breakfast. Without that helper, I haven't ate since breakfast reads as nonstandard.
Describing something completed before another past moment? The helper verb still takes eaten: She had already eaten when I arrived. Even with had, the participle stays eaten, never eated or plain ate.
Both ate and eaten work here because the sentence works either way, and eated never does. Say He ate the last slice when you're talking about a finished past action, or He has eaten the last slice when the result matters now: there's no slice left for you. But eated isn't a word in standard English in either slot. It looks like a natural guess, since many verbs add -ed for the past, but eat is irregular, so its past form is ate and its participle is eaten.
One qualifier that changes the choice
If your sentence already has a helper verb, have, has, or had, that helper changes your choice: the verb that follows must be eaten, never ate. I have ate reads as an error in careful writing, so I have eaten my lunch is the standard wording.
Notice how the helper does the tense work. In She had eaten before I arrived, the had points to the earlier event, so the participle eaten follows it. Without a helper, the plain past takes over, and the standard form is ate: She ate before I arrived.
You can test any sentence with one question: does a helper sit before the verb? If yes, write eaten. If no, write ate. They've eaten and They ate are both fine; They've ate is not.