With a strong enough box? The A+ can be built up to give some serious power in turbo form. It's more than possible to get a reliable 180-200bhp from a 1293 or 1380cc A+, albeit at a high price! But putting this kind of power through a normal 4speed Mini gearbox, and expecting it to last more than 5min's is not! Avonbar racing have built 1293cc A+ engines with all steel internals, and T25 turbos to give up to about 250bhp now. I do agree that a 200bhp A-series isnt going to last forever, and it probably won't reach 50'000miles, but it can be done, and a few people have 200bhp+ turbo mini's.
I don't see the need for that much power in a Mini however, as even a mildly tuned 110-115bhp metro turbo engine would really make a mini shift well!