No, he explicitly mentions that Lin and Ash getting on with it is cheating. Which is... odd for me.
That definition of cheating for him/her would be "having sex with anyone outside of the couple", which would necessitate that the main character is cheating on everyone with everyone. I think. I might be wrong though.
I think the definition of cheating would be "having sex outside of the relationship", which in this case is, what, like a dozen or so women and a guy. Atypical relationship, but hey, considering that some of the women are literally not even human (Lin is an elf, Maria is half, and Ashley is debatable, Android is not even biological, but just because they are not Homo Sapiens, that doesn't make them not people), it's not exactly an exclusive club to be fair.