No, They most definitely aren't yet as already stated by Valorum. In addition to his comprehensive answer, there were initial plans on making this happen.
There was a deleted scene in the movie which was going to make it happen however, that scene did not make the final cut.
Twitter user @Nick_wyld tweeted at director Rich Moore an image from deviant art featuring Nick meeting Judy's parents and she introducing him as her boyfriend.
The Image from Deviant art from Lyrin93:
The actual Tweet:
Rich Moore confirmed that there was a similar scene in the movie but it was later dropped. He also stated that it may be included in blu ray version.
Rich Moore's actual tweet:
Director also confirmed the friends-only relationship of Judy and Nick when a fan asked him on Twitter:
UPDATE: In Light of Valorum's finds on DVD, it appears that when Director said that there was a similar scene, he might not have meant completely similar with depiction of a romantic connection between the two characters. However, it is also possible that they did not add the said scene in Blu ray either as the director said they might include the scene but did not state that they will definitely do that. Nevertheless, the similarities between the supposed deleted scene and the extra scene valorum found are very convincing.