I don't know.
If the resulting side-effects will be less than the side-effects projected for using other means (and potentially an extended period of oil exiting the hole), then yes.
But I would want to know that it would be at least 80-90% sure to close the hole.
Sometimes I think we're alone. Sometimes I think we're not. In either case, the thought is staggering. ~ R. Buckminster Fuller
I don't have enough information on this to make an informed answer. Would a nuke have a serious chance of actually working? If it failed to close the wellhead, would it then be leaking oil contaminated with nuclear fallout? What would be the long-term effects of setting off a nuke at those depths?
If you build a man a fire, he'll be warm for a day.
If you set a man on fire, he'll be warm for the rest of his life.
You are assuming that it would not cause the leak point to become enlarged.
Too many assumptions.
Perhaps it might be better to ask the Russians who are reported to have dealt with similar problems in a similar manner.
An energy yield of a few kilotons is not going to gouge a huge crater in the sea floor. What it will do is fracture the near-surface sea-bed and collapse the bore. At worst case, the leak will be significantly slowed.
It can't get worse than the present Do-Nothing Administrations efforts to date.