In theory, yes because you would not have a 3 year or 10 year bar, but two issues again. Number one, you would never be able to use an ESTA ever again even with a 1 day overstay. Number two, you would still have to convince the visa officer that your overstay was brief, reasonable and would not happen again. If you are not able to convince them, then they will not issue you the visa because you violated the ESTA and they think you may violate a future visa as well. So perhaps if you overstayed a few weeks, you could do it, but I doubt it if you overstayed a few months.
And about your green card question, you are wrong if you apply while you are out of status, or while on an ESTA UNLESS you are married to a U.S. Citizen, have a U.S. Citizen over 21, or you are under 21 and single and have a U.S. Citizen parent.
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