Yes. He's become like this when he's growing older.
But usually during the times when he sucks his own fingers at the same time, he's very distracted and he can't feed very well.
Worse still, sometimes he sucks both thumbs when he's feeding!
When I try to pull his fingers out, he'd become angry!
My daughter is the same, nurse and suck her index finger or thumb at the same time. SOmetimes even both index fingers. I find her look to be so funny. She will fall asleep this way when nursing so I usually pull her finger out so that she wake up a bit and take in more milk.