Bubba, no t3 will not throw you out of ketosis. Yes Ketosis can slow down metabolism. However, if one's thyroid hormones remain constant, via synthetic thyroid hormones (t3), then you will burn more calories the deeper in ketosis you are. This is a longer explination than I care to type today, but it has to do with expelling unburned calories in the form of ketoes via urine, feces, sweat, breath etc.