Yes. Most people drop out after the first semester if they get into a US Uni.

Aren’t there some schools that don’t allow transfer students - what if you get caught?

For most schools (such as Harvard, linked below), you are not considered a transfer student until you’ve "completed at least one continuous academic year in a full-time degree program at one college."
https://college.harvard.edu/admissions/application-process/transferring-harvard-college

However, it would be best to double check the transfer criteria of the US college you’re interested in just in case.

Thank you for your insight. Do you think it’s plausible for me to attend a NZ university and not declare it, even if the US university I’m wanting to apply considers students who have done “coursework” at a university is considered as transfer students?

Every year a lot of students do opt to do that and US universities tend to give a wider berth to people in the Southern Hemisphere but I always would recommend checking the rules of the specific university in question and adhering to them explicitly.

Have you considered pursuing an internship or learning a language or something else in that interim period?