Julian
Personally
(1) I would tell ATC (it they didn't know) of the CB cell in the go-around track,
(2) I would negotiate with them what I would do in the event of a go-around and what would be acceptable to them, this would obviously be subject to terrain,
(3) If that required an early turn before the threshold, then I would advise them of the need for landing clearance at x nm,
(4) If all of the above agreed I would be prepared to continue the approach and land.
As a rider to all the above, I would consider fuel state and the general weather pattern and the speed of movement of the cells. If delaying the approach for 10-15 minutes would 'solve' the problem, then I would also have that option.
To answer your questions,
'Is it permissable?' YES
'Can the G/A procedures be altered?' YES
HTH