Precisely. The fun + learning balance is the most important thing. If the kids want to play, they should be playing.
Though you can be a little clever and come up with fun training exercises that can be practiced Player. vs Player and after letting them exhaust their energy on it, start a lesson and teach them how to play those positions better.
A few of my favorites are:
1. Pawn Battle:
http://www.kenilworthchessclub.org/media/Pawn_Battle_Strategies.pdf
2. Queen vs. Knight. Place a queen on any corner and the knight anywhere on the center where it is not attacked. Take turns (queen to move first) until the Queen captures the Knight. This exercise forces "one move ahead" thinking ... you won't solve it if you just make knee-jerk moves. Ask the students how the Knight should play (stay in the center, avoid the RIM!!!) and how the Queen should play ( figure out where the knight can escape to and cover those squares)
3. The untouchable King: After perfecting Queen + King vs King mates, set up a position as follows and ask them to Play White and try to mate without moving the White king. ( I love hearing them say "Oh, this is easy" before I get to finish telling them the complete problem :) )
Remember, it's easy to find something fun that challenges them as well.
I'm coaching a group of 20 elementary school students (beginners) for one hour a week on Thursday. We've met twice so far, covering the board, pieces and how they move, and the rules pertaining to checkmate. We haven't covered castling or en passant yet. Today we will be looking at simple checkmating patterns such as supported queen mates and double rook mates. This will more than likely take up the whole hour.
My concern is that some of the kids complained the first class about how boring it was because the already "knew" how to play. So last week I rushed through the lesson on checkmating and stalemating in order for the kids to have time to play. After watching them play, it became obvious that even though the ones complaining knew how the pieces move, they have absolutely no idea of how to play chess. In thirty minutes most of them had not even captured a piece! So at this point, wouldn't it be more important for them to learn how to play rather than spending a lot of time moving pieces around the board?