I can completely see this happening, to be honest, & I teach in an international school with 60 in a year group, so teachers know all the existing students.
Rock up to tutor time: 'sir, this is Omar. He's not on the register yet but Mr Brown asked me to look after him. He's shadowing my timetable'.
Genuine Omars happen all the time.
Off to maths.
'Miss, this is Omar - he's new, they haven't decided what set he's in yet, he's just shadowing me today.' OK then.
Rinse & repeat all day.
We are 3 weeks in & I've still, as a sixth form tutor, got kids on my register who I know perfectly well have been at boarding school in England for the last fortnight. Parents haven't filled in the 'removed from roll' paperwork in case it doesn't work out.
I've got new scholarship entry kids in my IB class that I do know about, but wouldn't have recognised from Adam on day one. Also one listed as doing HL with me who changed her option to SL, then dithered a bit, so is still on my class list.
I've had 2 emails today about new students in KS4 who were supposed to be joining my y10 class, but then between that email & data arriving from precious school were assigned a different group, whose teacher had no idea to expect them.
This is in a highly security conscious country where the kids are bussed in past security guards.
It could absolutely happen.