Well, as I understand black holes, which admittedly, is probably a fair bit out of date, collapsing into a Black Hole won't increase the gravitational effect of Betelguise in any way, it'll still have the same gravitic strength it always had, it'll just be compacted into a much smaller focus.
For example, if every last molecule of the Sun was instantly collapsed down until it formed a black hole, it would kill life on Earth, but the Earth itself would just keep orbitting the tiny black hole as it's centre of gravity, because the strength of the gravity would be the same.