Deferring to do a masters is fairly common. It really depends on your firm’s policy on this and whether they would make you go through a final round interview again next year (not unknown). You’d need to speak to the firm either in a VS exit interview or post offer to see the chances of that. A fair number of people defer their places across firms each year for masters study or something else, so this is not unknown and will be a common question recruitment teams get during schemes or after offers are made.
The transferring to the US office is unlikely though. It is not unknown but is exceptionally rare and when it does happen you need to be the best of the best candidate. Even when you do, you typically have to go through the US recruitment process still, just with a recommendation from the U.K. office.
Work permits are not straight forward either, so even if they did want to offer you a place in NY it may not be as simple as that if you don’t have the right to work in the US. Your profile is also not typical to US candidates, most will have a JD rather than an LLM, and so you are competing in a different student market. As a LLM student, you typically need something else significant to your profile to compete with the JD students with significant profiles. Your masters would need to be at a prominent US law school and you’d probably need to network effectively during your masters you strengthen your chances of converting to the US office or finding another US firm to work for.
You’d obviously also need to pass the NY Bar.
Most people take the view that it is easier to qualify in the U.K. and then move laterally to the US either on a trainee secondment or as an associate (either short term, long term or permanently). However, you’ll be in an environment where other people may also want the same (especially in a US firm). How likely you are to get a move across, really depends on a diverse range of circumstances, many of which will be completely out of your control.