They would initially lose weight, but recalculating their caloric intake based on TDEE would not be effective at continuing or maintaining weight loss because their body would not burn that amount of calories.
Most replies are about the challenges of going from obese to a healthy weight because your post is about ozempic/wegovy. This is only meant to be used in the treatment for obese people, not overweight people or people who have just overindulged and have a few pounds to lose. It’s a totally different ball game.
In the scenario you describe, where someone has just been making a few bad food choices and gained ‘a bit’, the person is unlikely to have the metabolic and hormonal dysfunction which obese people have.
The body has a set point it fights to defend - if someone has just gained ‘a bit’, it’s highly unlikely this set point would have changed. It does not tend to change in adulthood - it is set during puberty, and the only times it can change after this point is during pregnancy, or if someone gains a significant amount of weight.
it’s also linked to the number of individual fat cells which someone has. If someone was a healthy weight and gained a bit, and has never been obese during their adult life, they are likely to have a normal number of fat cells. If they gain weight, their individual fat cells will get larger/more full, but they will not actually grow any new fat cells. Their fat cells being ‘full’ essentially set the body up to lose the extra weight. Obese people have an excessive number of fat cells - which again, is usually set during childhood, and cannot ever change. You can reduce the individual size of fat cells, but you cannot reduce the number of fat cells you actually have (barring liposuction which has its own risks). Fat cells are metabolically active, and contribute to the hormones around satiety and hunger which cause the regain effect in obese individuals. So when an obese individual gets to a healthy weight, they still have a hugely excessive amount of individual fat cells compared to someone who has never been obese - and each of their individual fat cells have just been shrunk, which makes the body believe there is some kind of famine, which leads to the huge drop in metabolism which happens.
You’re completely right that the metabolism slowing is likely to happen regardless of how weight loss occurs - which I presume is why it is prescribed as a lifetime medication in the US. But as it directly impacts the hormonal profile, it may counteract some of the usual hormonal rebounds and effects which happen with significant weight loss - I’m sure more research will come out about this, as time goes on and people who use ozempic/wegovy can be studied long term.