I don't believe tea would cause an increase in blood sugar, unless it was sweetened. In fact, recently, at my last doctor's appointment, my doctor told me to cut out coffee all together. I have high cholesterol and high blood pressure.
I cut coffee out completely. I used to drink coffee without sugar too.
But now I drink tea, cold or hot. However, with hot tea I do add flavored cream which has sugar in it.
Then there is pearl tea. I love that stuff, but that might have some sugar in it. I'm not sure.
Regular tea though without any sugar wouldn't increase blood sugar that I know of.