Is there anyway hashimotos thyroiditis or hypothyroidism could cause a false negative pregnancy test?

No. Pregnancy tests look for a hormone called human chorionic gonadotropin, or hcg. It is made by the placenta, and levels should not be affected by anything going on in the thyroid.
See below. Hypothyroidism would not cause a negative pregnancy test, but it can make getting pregnant harder. If you wish to have a baby and are hypothyroid, you should be on replacement medication.
Have a healthy diet, exercise, drink plenty of water, have safe sex, and get HPV vaccine. Wish you good health!