D.G.
Yes you can have celiac even if blood tests are negative. The only definitive test is a biopsy showing intestinal damage. My nephew has celiac as dx'd via biopsy and if I remember correctly his blood tests were inconclusive.
Talk to their pediatrician before considering a gluten free trial, since you have to be eating gluten for accurate test results. (biopsy and blood test). You may want to consider thyroid testing since that can also cause failure to thrive. And check for anemia too. (anemia can be a symptom of celiac and can cause dark under-eye circles).