The simple answer is no. Free-to-play players don’t have access to the Pest Control minigame as this is for members only. So even if the FTP players were to mark off all the criteria in the hard Western Provinces diary, there would be no means of getting the Knight Recommendation Points needed. Plus, these items are untradable, so you won’t be able to find these items on the Grand Exchange. So if you want the Elite Void Armour, you’ll need to sign up for an RS membership.