That's a new one to me.
I wouldn't try it in my car. Why?
One reason is because it's virtually *impossible* to drain all the coolant out, so there would always be a little baking soda left behind.
Another reason: baking soda is a base(as opposed to an acid. Lye is a *strong* base). Did you ever see what happens when aluminum comes in contact with a strong lye solution?
When I was a kid Dad filled balloons with...but that's another story!
Any aluminum in your cooling system(in my case, the head, intake manifold, & radiator!) might not be harmed at all by traces of leftover baking soda, but I wouldn't want to take the chance. It would be in there a long time at a high temperature. I may be wrong, but it sounds like asking for trouble to me.
Unless you have good reason to think your cooling system is really gunky, just drain, fill with clean water, run till warm, drain again. Do it several times if you like, or think it's needed.
If want to use a flushing agent, it might be safer to pay a few $$ for a purpose made product that's guaranteed safe for your cooling system.