The announcer, booster and publicist badges are awarded for sharing questions (or answers, as has been discussed in this question). According to their descriptions, only clicks from outside the Stack Exchange network count toward the badges.
Is MathOverflow part of the Stack Exchange network?
I have a question on MO which contains a link to a question on MSE, but earning one of the badges above for that link seems dishonest.
39599
from it: e.g. link tohttp://math.stackexchange.com/q/194749/
instead ofhttp://math.stackexchange.com/q/194749/39599
. See here. $\endgroup$