Yes. Red shirts and eligibility years are sport independent. That’s also why Kyler Murray can go pro in baseball, lose his baseball eligibility, and still play football. Ricky Williams and Ced Benson did a similar thing.
I coached a kid who went D1 in football and track. Staggered his redshirt years (football his freshman year, track junior year), went to school (all paid for) and left in 6 yrs with an MBA.