Re: the question in your title...absolutely not.
Blood work does not necessarily rule out celiac disease (autoimmune gluten intolerance). Only a small intestine biopsy can do that.
I've done pretty extensive research on the gluten issue, and I have never found a study that established a link between gluten and Hashi's. There are many people who claim there's a link, but I have seen nothing concrete.
Since there is no proven link, my advice (I have Hashi's and eat gluten) is that if gluten bothers you, then avoid it. If not, have at it. I was gluten free for almost a year (I did it for other reasons than my Hashi's). I didn't expect it to improve my Hashi's, and it didn't.
Did you see that last week, I believe, that the British researcher, who started the gluten free craze with his study, admitted that his study was seriously flawed and retracted all his recommendations?
We've had many discussions on this forum about the issue. If you search the archives, you'll find a lot of information, both pro and con. I suggest you start with this thread:
http://www.medhelp.org/posts/Thyroid-Disorders/Why-Do-I-Still-Have-Thyroid-Symptoms--When-My-Lab-Tests-are-Normal-by-Datis-Kharrazian/show/1299599