No, if your Samsung S22 Ultra has noticeable screen burn, most likely they will significantly reduce the trade-in value or even refuse it entirely, as screen burn is considered a major defect and not accepted under normal trade-in conditions; even slight signs of burn-in can be detected during inspection and affect the value of your phone.
They're very strict in terms of their trade in. A lot can be argued on the subject. It may be worth speaking to live chat/ phone to get samsungs opinion
Screen burn is caused by keeping a static image on the screen for a long time, it why with the always on display it's not really noticeable but items will move a little bit every so often and it also uses less power.
If it is the likes of the top bar burnt into the screen the cause of this will be keeping the screen switched on for prolonged periods with the top bar visible, this is why in most apps the top bar actually hides.
As a result screen burn generally is seen as user fault as it is only caused when the user does something to hold a static image on the screen for prolonged times, under general use you should never see burn in and like above I've used Samsung phones for years now keeping them about 2 years each and I've never seen screen burn.