After dissolving sugar in a cup of hot coffee, could you ever get that sugar back in it s original form?

Not original form, no but perhaps if you do a simple kids science experiment you could get it back in crystal form. Simply dangle a string from a pencil over the cup until the coffee evaporates, leaving a crystal structure attatched to the string.

I guess if you could evaporate the water, then use chemicals to remove any coffee components from the dried stuff, but that would take a lab and science.

Yes. You boil the water until nothing is left but the sugar.