Going by the original Reddit definition of incel, I would say no.
He had an ex-girlfriend, incels are too timid to even ask a girl out in most cases. Also, the word incel is just a derogatory description of a shy, ackward, and unattractive guy. The term is an empowerment mechanism, especially with the emphasis on the virgin stigma.
In my opinion, we need more emphasis on teenagers and young adults maintaining their purity, rather than promoting behaviors that make fun of kids who are virgins.
My husband and I both believe that it's a bad thing for women and men alike, if they get this idea that "everybody's doin' it" and therefore if they themselves are not, it must be because they're sexually retarded or they're being rejected & disrespected.
We live in such a sexually distorted society.