Can I put a little baking soda in my TT toilet?

I see no reason why could not use baking soda. If you can use baking soda to brush your teeth with, I don't think it will hurt anything in your RV. But how much it will help is anyone's guess.

If it were mine, I'd go ahead and use a garden hose and wash the toilet and tank out. Catch the black tank contents in a bucket and dump it down the toilet in your house, unless you live in the country and can dump on your ground, bury it in a hole and cover it up. Let your tank drain until nothing else comes out. Then pour some pink-stuff (RV antifreeze) down the toilet to keep the valves wet so they will not dry out. At the same time, you can drop one of those chemical pouches in there too. As long as you drain the black tank immediately, you'll not have anything freeze up.

If you cannot use a garden hose,then haul buckets of water from your house and pour it down the toilet, and use the water to clean everything. You can even use hot water from the house if you use the bucket-brigade to bring in the water. Just drain the black tank immediately so nothing has time to freeze.

That's what I'd do.

Sure, baking soda is OK. Folks put all kinds of nastier stuff in their tanks to knock down the smell. You may want to make sure your tank vent is open to the roof from the tank. Run some water into it to check.