It would bother me if my T ate during a session, regardless of if she offered food to me or not. I am self-conscious enough already, I don't need her being distracted by anything. Thankfully my T is awesome at being attentive and not giving me any reason to doubt that she isn't interested or isn't paying attention to to me.

She occasionally asks me if I want water but it is only on days where she also has a bottle in the room. I figure it's common courtesy if she is going to be drinking it in front of me. However, I always decline