Is it safe to use the tip of a hot glue gun to melt crayons?
It will work, as high temperatures melt the crayons, regardless of the device you use, but in all cases I'd suggest doing it in a well-ventilated room or outside, as the fumes are a little toxic.   

Also note that holding the crayon in one hand while doing so is asking for trouble: wear a glove, or attach the crayon sturdily to something. 

I'm sure crayons won't damage the glue gun more extremely than the glues it is used for (I mean, the tip of the hot glue gun is made to withstand damage).