There is a relationship, this despite there being so many different No.2's throughout ‘the Prisoner’ series, and that was the given reason behind there being so many different No.2's, so that No.6 would be unable to strike up a relationship with him or her.
But it wasn't quite that was it? Because I believe we can say, that there was certainly a rapport between No.2 and No.6 during the episode of ‘The Chimes of Big Ben,’ and such rapports do not arise over night. And so to resolve this to any satisfactory conclusion, much depends upon the time between the end of Arrival and the first day of ‘The Chimes of Big Ben’ for example. Because we can say that there must have been a gap of some time between the end of ‘Arrival’ and ‘The Chimes of Big Ben,’ as the new No.2 wouldn't just arrive for the closing moments of that episode. The man had only just commenced his term of office, and in this, No.2 of ‘The Chimes of Big Ben’ might very well have been there for a few days before Chimes began. Because I think it is wrong, and far more interesting not to see the one episode commencing straight away after its predecessor. Of course this rapport between No.2 and No.6, which they both seemed to enjoy, could have been established before their encounter in the village, of prior knowledge perhaps, or simply a case of No.6's reputation going before him? After all No.2 told No.6 that he was glad that he is here. After all during the time in the embryo room of ‘Once Upon A Time,’ No.6 admitted that he knows No.2 "In my mind, in my mind... you're smart!"
This relationship between Numbers 6 and 2 was rekindled during the episode of ‘Once Upon A Time,’ No.2 even admitted in the embryo room that time "I'm beginning to like him." And after escaping the village, and upon their return to
, they even parted on good terms in London Parliament Square.
But there was not one No.2 with which No.6 enjoyed a rapport with, after all by the time of ‘The Genera’l No.2 and No.6 were old friends from way back, since ‘A B and C’ in fact.
And then there's that elfin looking No.2 of ‘Dance of the Dead,’ a female yes, and "Never trust a female, not even of the four legged variety" being No.6's golden rule. Ah but this female No.2 isn't all that feminine is she, and that just might be the reason behind his rapport with her, her lack of femininity. But on the other hand perhaps not, after all there had been Alison-No.24, and later Monique, the watchmakers daughter-No.50.
So yes, despite the attempt to try and halt any relationship developing between No.6 and No.2, the fact that once they have failed in their attempt with No.2, or his or her term of office had reached its end, they were removed from office. This through the possibility that any given No.2 might, just might, begin to show a lack of apathy, thereby showing a possible likeness towards No.6 and in that to assist him to escape.
So yes, even so there is time for No.6 to build up a rapport with No.2, which is only dependant upon the person at the time, and the length of time we don't see between episodes of ‘the Prisoner.’
Be seeing you