he sounds very bright, but he also sounds rude and bossy. 
children who lack social skills need support whether they are gifted or not, so it might make sense to separate out these things in your mind and deal with them differently.
yes, ask school to refer to ep for testing if you think they need clarification of how bright he is, or you feel that educationally they are not differentiating appropriately. if they are, it might not be necessary.
but also ask if they are able to work on some social skills targets (these can form part of an iep if they want to formalise the process.) if they want to do an iep to help with target setting for g&t or whatever and you feel that you help them differentiate appropriately, then also fine.
if it helps, ds1 is a bit similar. he would want to debate religion and evolution at 6/7 due to the obvious curriculum conflict. at three he was working out shopping and change, and how many different ways you could pay with a pocket full of assorted coins. he's also socially quirky and has some definite anxieties. his teachers usually just suggest he has some sort of einstein thang going on, and so don't expect him to bother himself to do the same work as everyone else (which imvho opinion doesn't help at all). so essentially he's been encouraged to only bother to write down answers to the q's he deigns to answer. this year's teacher wants him to sort his life out though. so does the new paed. for which i am extremely grateful because it is becoming impossible to live with.
various dx have been suggested - add,adhd,odd, aspergers, asd but none fit particularly. he's just bright and a bit odd (in the odd sense, rather than opp defiant lol). to be frank, we take any help we are offered but there isn't much as he's bright enough to get awqy with not following the norms. i'd be a bit sceptical about a family support worker, but it shows willing, and recognises that they do have real concerns about his social abilities.
dd2 is 8 and extremely bright and also a bit odd socially, but she has cp, so it's tricky to sort the wood from the trees really. dd1 is bright (regional gifted programme, mentorship programme etc) but absolutely 100% nt as far as social skills - understands all social nuances and how to behaqve, lots of friends. all kids are different and some need help. it's feck all to do with parenting, and some outside guidance might be useful! it's somewhere to start, anyway. you can always say no thanks later.
and you might want to lose the prejudice about kids with issues and assumptions about their background.