Is the kinetic energy turning into activation energy when the reaction takes place?
You got it right: when the reaction takes place, the kinetic energy of the reacting particles turns smaller because some of it is (sort of) spent on activation energy. It is just that the "when" in question is incredibly short.

Imagine two tennis balls flying at great speed and hitting each other head on. Sure enough, they will bounce off each other and fly in the opposite directions with the same speed. Some time into the collision, there must be an instant when they are not flying anywhere; their speed is 0, and so is kinetic energy. All energy they possessed has converted into the potential energy of elastic deformation, only to return into kinetic energy again really soon.

Same thing with molecules, except they are way smaller and fly way faster. Also, there might or might not be a reaction, and if it happens, then the kinetic energy of the molecules after the collision will not be the same as before. It may be greater, or it may be smaller; that's how exothermic and endothermic reactions happen.

So it goes.