No.
Pagan:
from Late Latin paganus "pagan," in classical Latin "villager, rustic; civilian, non-combatant" noun use of adjective meaning "of the country, of a village,"
Online Etymological Dictionary
Middle English, from Late Latin pāgānus, from Latin, country-dweller, civilian, from pāgus, country, rural district; see pag- in the Appendix of Indo-European roots.
American Heritage Dictionary
Propaganda:
"committee of cardinals in charge of Catholic missionary work," short for Congregatio de Propaganda Fide "congregation for propagating the faith," a committee of cardinals established 1622 by Gregory XV to supervise foreign missions.
Online Etymological Dictionary
from Latin prōpāgandā, ablative feminine gerundive of prōpāgāre, to propagate; see PROPAGATE.
American Heritage Dictionary
But also yes.
Ultimately both from Proto-Indo European pag-:
pagan, peasant, from Latin pāgus, "boundary staked out on the ground," district, village, country;
propagate, from Latin prōpāgāre, to propagate (< "to fix before"; prō‑, before, in front; see per1);
The American Heritage Dictionary Indo-European Roots