Is it it normal to imitate the accent of the song you're singing along to?

Depends on the song.

If in doubt I sing along in a Southern USA accent.

There are no famous singers with my accent and honestly I see why.

Yeah I love to imitate scottish and brittish in songs. Attractive accents.

Singing is it's own accent.

Normal.

Yeah I always try to imitate the artist as close as possible, including their accent. Other times I sing in my own accent (cockney) just for the laugh, to see what it sounds like.

I always sing in my own accent.

Whenever I listen to German music though, and it's a song sung in Plattdeutsch, I'll always stubbornly try to sing along in Hochdeutsch because that's the German I learned in school (and mostly forgot anyway).