Most likely it won't. You also won't get the full features with a normal stylus that you would with the "s" pen.
If you have lost it or it is not working, you will be able to find them on samsung.com.
Actually, the "stylus" I am referring to is a genuine Samsung S Pen that I bought for my Note 2 because I thought I had lost my original. I found the "lost" pen so now I have 2. If I upgrade to the Note 3 will the spare that I currently own work with the Note 3?