Sonically, Complicated isn't anything close to punk. When I think of punk, I think of fast tempos, driving drums, frantic guitars. Complicated has none of those things; it's super laid-back and mellow. It's a good song, but to me it's about as far from punk as you can get.
She has other songs that are more reminiscent of pop-punk on later releases (He Wasn't, most songs on The Best Damn Thing), but if you listen to Let Go in full, there really isn't anything else that sounds like Sk8er Boi. She has heavier songs (Losing Grip, Unwanted), ballads (I'm With You, Tomorrow) and a lot more mellow songs, but nothing else that screams 'punk'.
I don't want to get bogged down in genre debates - to me, good music is good music irrespective of what arbitrary label people want to attach to it - but I just find it peculiar that her most famous song isn't indicative of her overall sound back then.
As for whether she was trying to be a punk or not, in all honesty I don't think she was trying to be anything other than herself. She had a wide range of influences at the time including punk bands, heavier bands and singer-songwriters, and this is reflected in her music as well as her image. To me, she was simply a young girl figuring out her identity.
