Yes. Visible pet hair is one of the top reasons used-car buyers walk away or lowball, and the cost of professional removal is recouped many times over against the price hit a hair-coated car takes at trade-in or private sale. Even buyers who own pets themselves discount visibly hairy cars because they assume embedded odor and stains.
Sequence we recommend: book the pet hair removal as part of a Gold or Platinum tier 1 to 2 weeks before listing. The full detail addresses everything a buyer inspects (carpets, seat fabric, headliner, dashboard, exterior paint), and the result holds for the photo session, dealership inspection, and test drives. Adding the engine bay detail on top signals "well-maintained" to inspectors and bumps perceived value further.
Honest take: pet hair removal alone (without the broader interior cleanup) is rarely the right move for a sale. Buyers see the whole car. We spec the right package combination during the quote so you spend on what actually moves the resale price.