I'm not sure about this,however,there's another sugar called 饴 in China much earlier than 唐dynasty,but as you think the character 糖 did not exist in earlier China. fiorenza said it is a character from 《说文解字》，it isn't correct,actually it is a character from 《广韵》 that was written in Song dynasty,说文解字 was written in Han dynasty which is earlier than Tang dynasty,all that we can know is the character has something to do with rice(米). and I found that China is an original place of sugar production,so the character may related to Tang dynasty,but not the way you think:)

Hello, I majored in Chinese. In the Dictionary Explain Words(《說文解字》) said that "糖，飴也"，it means this word "糖" means candy, more like maltase(麥芽糖) now. The two different words and means one thing. (But 糖means maltase, but 飴 has more meaning.)

we get some discuss,then we can get the answer。

sorry,my asnwer isn't correct,and thanks for fiorenza.

These two words have nothing to do with each other,