Artem definitely fancies Kara, and the feeling is mutual imo. There is nothing fake about either of them - that's their charm.
If they're training as many hours as they can, even training back at Kara's Mums and Dads, they might be a bit too knackered to do anything else.
I think Artem (and Kara) takes this process seriously and feels the responsibility to get Kara as far in the comp as he can. It makes sense to me that he wouldn't - how ever much he wants to - let anything jeopardise that.
Also, despite being in such public professions, I think they're private people and were only forced to mention the possibility of a date after Strictly to get the media scum off their backs.