No, he did not consider himself an "outsider" by staging a civil rights protest in Birmingham.
Reasons:
1) He and several members of his staff were INVITED by an affiliate of Southern Christian Leadership Conference to be on call to engage in a nonviolent direct action program when necessary.
2) He was compelled to carry the gospel of freedom beyond his own home town.
3) "Anyone who lives inside the United States can never be considered an outsider anywhere within its bounds." - MLK Jr.