It's not really an "official" record. I suppose it's more of an interesting statistic that commentators bring up every once in a while. But, technically, it's still a record as Kane's eliminated more guys in any single Royal Rumble match than anyone else.
As for whether or not Reigns should break it, I think that's the direction they're going in. On Old School Raw this coming Monday, Punk goes one on one with Roman Reigns. Like Rollins, we haven't seen Reigns featured in very many singles matches, so this is his opportunity to really make an impact. As a result, I'm thinking that Reigns either winds up beating Punk, is accidentally cost the match by Ambrose's loose cannon behavior or is purposely cost the match by Ambrose under the pretense of it being an accident. The ending of the match will be almost certainly play a role in the growing rift within the group. If Reigns looks dominant here, I expect him to at least tie Kane's record of 11 eliminations, if not surpass it. If WWE is genuinely serious about elevating Reigns as a singles guy, then it's a good way to make an impression. I agree that it might be a little too soon but, at the same time, part of what's made The Shield so entertaining for the past 13 or 14 months is the consistently strong booking they've gotten. They've scored huge wins, the vast majority of them clean in fact, over the biggest names in the company. As a result, they've been established and accepted by fans as major players. Reigns having a strong booking at the Royal Rumble would only be following a formula that's definitely paid off.