In my experience, no, though I have read otherwise, but I have presided over many a change in registrant with no ill effect. Often when a site's registration is changed, so is the hosting, and often structure and content is changed, all at the same time, and conventional
SEO wisdom says too much change at once can affect rankings badly - but *not* necessarily. If the changes are generally positive - great new content, and an easier to navigate,
SEO-friendlier structure, the rankings are likely to improve enormously. I have done the
SEO for several redesigns and launches of sites in the past year where content and structure changed much, as well as hosting and all showed marked improvement less than a month from launch .. some within days ... hope that helps ... I am sure others will ring in on Monday.
Cheers, MJ