MOT wise, it really depends how much it's blowing.
I'll usually just advise "minor leak of exhaust gas" unless it's really bad, but bear in mind it'll likely affect the emissions reading and fail that way.
Either way, not replacing the stud/s is far from ideal as it'll eventually burn the manifold gasket out, and you'll be back to square one.
Chris is absolutely correct in saying that it's possible to wreck the head if not done right.
That said, I was an exhaust fitter back in the late 80's early 90's and must have drilled and tapped a thousand snapped studs in situ, but I had the experience, plus there was a ton more room under bonnet than there is today.
Get it done by a professional