You're good to go.
Appleseed doesn't care what sight you have on your gun, they're just happy you're there, carrying on an American tradition and learning to become a better marksman. When I took mine, there were guys there with optics, scopes, peep sights, blade sights, you name it, it was there.
My Appleseed instructor tended to favor peep sights like the ones used on Garands and AR-15's but the lessons learned can be applied to whatever you're shooting. You're 10/22 is perfect for the shoot. I used my AK on day one and came close to achieving Rifleman score but couldn't quite get there. Day two I switched to my 10/22 and got my Rifleman patch after the first course of fire. Your rifle is perfect just the way it is. Make sure it's sighted in and your familiar with it parts and operation. Bring at least 200-250 rounds per day. A 500-round brick of your guns favorite ammo is a worthwhile investment. Don't waste your money on a brick of $15 Remington, spend $30 or $40 (or $50) on a good brick of Wolf or SK match ammo, Aquila standard velocity match or whatever your gun shoots best.
Suggestions: Bring extra mags. One mag won't cut it, you'll need at least two, I'd recommend four. Bring a mat to lay on. If you don't have one, you can buy one yard of carpetting at Lowes or Home Depot for around $3 or $4 per yard and it'll be around 6 feet long.
Bring knee pads and elbow pads. Sounds goofy but trust me...you'll need them. I had bloody elbows at the end of day one without them.
Go in rested and fed, stay hydrated, pay attention, and have fun.
You'll learn alot.