Any fridge is on 24/7/365, but still comes with a plug fitted.
But there is nothing wrong with hardwiring them into a switch fuse.... its just not standard
Basically, if its stuck to the wall, it doesnt come with a plug..... if its portable... it does.
And portable does include large, american style fridge freezers.
Either way, whether an appliance is plugged in or not isn't part of the original question.
Which, if i understand it, was
"can you just have a ring circuit, with no points on the ring itself, but unfused spurs coming off the ring, with points on the end of each spur"
And a very early answer was "yes, but it would be non-standard"
There's nothing in the regs to say you cant.