No, says the Arkansas Game and Fish Commission. Ownership of Arkansas real estate by a person living outside the state does not qualify the owner as a resident.
AGFC rules, long established, say. "A resident is any person who physically inhabits a bona fide residence within Arkansas for at least 60 days and declares themselves a full-time resident of Arkansas." There is no dual citizenship for purposes of hunting and fishing licenses.
Some liberal rules apply to college students and military personnel, though.
Full-time students enrolled in Arkansas can purchase annual resident sport licenses, so can resident foreign exchange students attending school outside of Arkansas; nonresident foreign exchange students attending school in Arkansas; residents of Arkansas enrolled as full-time students in colleges and universities outside of Arkansas; and nonresidents enrolled as full-time students in colleges and universities in Arkansas.
Military personnel on active duty and stationed in Arkansas can purchase resident sport privileges for hunting and fishing. Active duty servicemen and women who were Arkansas residents at the time they entered service also can purchase resident sport privileges for hunting and fishing, regardless of where they are stationed.