Upvote:2
The scenario you describe seems to be making more trouble for yourself than need be.
In order to enter the US with a UK passport you will need an ESTA (this applies to entry by all routes after October 1 2022). To apply for an ESTA you will need to declare all your citizenships, including your US one. If you state that you have US citizenship you will be denied an ESTA (since you don't need it). If you do not declare your US citizenship you will be guilty of deception, a crime that carries serious consequences even for a US citizen.
In any case your entry record will contain enough information that it can be linked to you and your US citizenship. Your US citizenship may not be immediately flagged at your entry, but anyone searching for your immigration records will be able to find out that you entered the US at the time you did. If you are looking to deceive authorities into thinking that you either did not leave the US, or did not enter the US, then that will almost certainly not stand up to any sort of scrutiny.
If the reason that you want to enter the US on your UK passport is that you do not have a current US passport then you are probably best off getting one.