Lock tite and sprocket

Without a doubt, Yes!

In fact, Kawasaki feels so strongly about it that if you order new OEM bolts for the sprocket, they come with lock tite (red) on the threads.

My Kawasaki sprocket nuts and other nuts on the bike have locking devices built right into the nut, similar to a nyloc,but better. They never come loose and don't require washers. If you have the standard nuts, loctite and lock washers are a must!

Be very careful when using a locking type nut. These items are ONE TIME ONLY items.
Once you remove them, they are done. It may well feel like they are locked the second time, but they will not be sufficiently locked. Threads can be destroyed during the first removal making them unsafe.

Lock nuts or "star" nuts will have a diamond or some sort of funny pattern on them to let you know they are locking nuts.
If all you have are the metal locking nuts when you reassemble a sprocket, you'd be better off using a new grade 5-8 bolt and using liquid loc-tite.

BTW...Nylocs, or nylon locking nuts, are ONE TIME USE ONLY as well. Never kid yourself and feel they are fine for a second use. They aren't.

The kind of nuts on my bike are not the star type. I don't know how to describe them, but there is a part inside the nut which holds tension. Most of the chasis uses these. I have reused them with no problems. the manual doesn't say anything about replacing them. better safe than sorry though, especially with the sprocket.

my friend had that problem on his crf450...apperently the previous owner hadn't used locktite or reused a bolt and when the bolts fell out of it(he lost 4 or 5 of them) it destroyed the entire wheel...better to be a cheap nut than 4 or 5 hundred dollar wheel.

I'll give you a very good reason to use lock tight! I forgot to use locktight on my old cr125 sprocket and all the bolts came out and the sprocket shot off the wheel like a bat out of hell! also i had a front sprocket shoot off b/c of the same reason.