The boost of experience gained by equipping the Experience Gem as well as the boost of skill experience and class mastery experience gained by equipping the Knowledge Gem still apply to an adjutant. Unlike the Pair Up system, adjutants cannot swap positions with the host unit mid-battle and they do not provide any stat boosts for the host unit.. The knowledge gem was really cool and helpful! Right up until Luckily I got another one in the same chapter, but sheesh. At least it wasn't my speed ring or somethin' like that.
For Fire Emblem: Three Houses on the Nintendo Switch, a GameFAQs message board topic titled "What does the Knowledge Gem actually do? (Spoilers, maybe?)".. The Knowledge Gem is also super helpful, making the process go by twice as fast. You can either give it to an Adjutant with a lead unit that will see a lot of combat, or field it on a lead unit and trade it around for some of your Player Phase actions.