Nope, it's only canon if you don't try and get Basil and Carlotta back together. Then again, they had a lot of issues, so who knows how long their happiness would last. The story is pre-relationship of course, I think it'll take a while for Basil to really open himself up again... but I think Min could be the one to do it!
The scenes mentioned, scene 45 is one you can see if you
a: don't get Basil and Carlotta back together, and
b: do Min's request on the job board.
The pic at the top is a peak of the CG from that scene!
Thanks for reading ^^