First of all they would have to play a minimum of 2 years in the UK to qualify for their national team, as well as having British citizenship (4 years if they have played for a different country before).
Secondly, the British tried this strategy back in the 1990's, granting citizenship to the top Canadians playing in the British league, which included some former AHL players with spot NHL duty. The result was that the Canadian-British players took all the top lines for the national team, and the British players gained no experience and the overall skill of the country declined as a result.
The British hockey federation realised that this was killing hockey in the country, and decided to stop using Canadians on the national team, going for an entire homegrown team, even if it meant they were not so good; in the long run (really long as it seems) it would help improve the quality of the team and skill level in the country.
To summarise, the British tried this as much as they could (can't just use NHLers who've never even been to the UK) and it weakened British hockey and didn't help improve the team. Went back to an all-British team, similar results, improved quality of hockey in the country.
Is the bolded part an IIHF rule? Last time I knew, anyone with one British parent was immediately eligible for a British passport, whether they've ever lived in the country or not, as is anyone born in the country. (Not that I avidly keep up to speed with these things).
You're right about the shift in policy towards "dual nationals" in the 90s. Playing such players got GB into Pool A of the worlds, but only for one year. Many of these players came to Britain after college. They needed to play seven years in the country to become eligible for citizenship, so most were at least 27 by the time they qualified.
At the time, most British clubs only used two lines, so the players really struggled to cope with stepping up to international hockey. Seven years of playing 40 to 50 minutes per game in a semi-professional league where teams practice twice a week isn't the best preparation for playing Canada, Russia and the rest.
Everyone knew the only way to get a stronger GB team involved improving the standard of local players so that every domestic team could consistenly roll three lines.
Inevitably, the dual national policy created tensions between Brits and Canadian-born players, which harmed team spirit. It didn't help matters that when Canada played GB, several GB players sang along to the Canadian national anthem. In the end, Tony Hand, Britain's best native player, became utterly disillusioned with the GB setup, withdrawing from the team for a few years.