In Northern Ireland people will say 'He went to Bohemia on holiday, so he did', or 'I need to do some shopping, so I do'. Is this correct English?
Yes, of course it is, but it's not normally found outside Ireland.
These parentheticals, tacked on to the ends of sentences, have the same pragmatic role as the pragmatic markers (veridical / emphasising / focusing) truly or in truth or the facts of the matter are (which are, however, usually put before the matrix sentence).
As to their grammaticality, it's almost certain that a panel of professors of linguistics would pronounce them 'not ungrammatical'.
As to the advisability of using them, the effect they would produce outside Ireland would be to convince a listener that the speaker was either from Ireland, or affecting an Irish style of speaking. If the latter, this might be considered highly inappropriate.
As an Englishman from the Midlands of England, I certainly regard this as perfectly good English. I find the addition of 'so he did'; 'so I can' etc. at the end of a sentence to be fascinating - not least because of the fluency with which it is done. It must be quite difficult, because one has to instantly recap what one has just said in order to get the right verb/tense etc. Try it yourself - it's not as easy as those from Northern Ireland make it sound.
This question led to some bitter-sweet comments, one was to the point : "Define correct English".
If English has no system of reference, it will progressively evolve like French, Italian, Spanish, Romanian and others : only partially understandable between each other, at least in writing, fairly easy to learn one of them if you already know another one, but no more.
I believe that the only one referential you may rely on is what is called "Oxford English", "BBC English", "Queen's / King's English". And when you speak it, you are understood all over the world, not the reverse.
You can see the damages on "Stack Exchange" itself :
I was down-voted a number of times for what I wrote, correct I believe in London, but not in the States, for instance the use of present perfect and preterit ;
whereas I never reacted, I was horrified by some American-English turns of phrasing which would never been accepted by an English teacher, or an European teacher of English. For instance, I read, from one American member with a very high reputation "never use whom" ; in the UK, mixing up "who" and "whom" would be a sign of deep illiteracy.
To answer the question, I would say "it is not correct English, but perhaps correct Irish, which is a dialect".
However, it is difficult to tell an American that he speaks just a dialect, and moreover an impoverished one (by far less vocabulary as compared with the man-in-the-street in the UK ; they compensate for that by using strong words).