Still Job/Shootout leader even if sent home booted?

Is the leader of a job or shootout still the leader if they are sent home booted?

For instance what happens with Meet the new boss?
Noon Job: Mark the town square. If successful, your leader permanently gets +1 influence and 1 control point. Ace this card whether or not the job succeeds.”

Does the job still succeed even if the leader is now home booted?
I assume that it does since I couldn’t find anything in the rules stating that the job fails if the leader is sent home booted, but I want to be 100% sure.

Thank you!

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Seen and under review!