Just to clear this up, I'm an mot tester and roadside breakdown tech. The spare tyre is not part of the mot, present or not, bald or not it doesn't matter. Its not a testable item
Also the spare wheel he's got, these newer space-saver wheels are, as has been said, much thinner and only designed to keep you moving to a place of safety or tyre replacement. The general rule of them is 50@50, 50 miles at 50mph. They are generally a life saver where the original tyre is torn or ripped. If you don't have one and it's an option for your car, it's a wise investment.
Some of the newer cars come with a bottle of sealant, all I can say is please don't use it. If you get a puncture and you have no spare tyre please call your breakdown cover, we can very often do a temporary plug repair if it a nail in the tread etc and if the tyre is beyond help we carry universal fit spare wheels. Also the jack that vehicles come with are downright dangerous and unstable, we don't call them suicide jacks for nothing. You risk serious injury or worse if the vehicle wobbles off it.
That sealant rarely works, defo won't if theres a physical hole in the tyre, it relies on the foreign object being in the tyre. Also once you use that sealant it scraps the tyre. Even if the puncture is totally repairable, the moment you put that sealant in the inside of the tyre gets coated, making a full repair impossible.