In the past, users have reported font size change tags appearing randomly in the text of the message being composed. You are right to raise the question about signatures because they also introduce invisible formatting. HTML can be complex it's hard to know exactly where your insertion point is.
Or use an HTML source viewer/editor to see where your cursor is, or what is being inserted for you. I still think that Stationery is useful because it explicitly defines styles, and some buffer blank lines are the best way to avoid travelling past invisible font tags.
I suspect our OP has discovered that his messages can look fine when being written but are all over the place in the recipient's mail program, because this setting can make TB hide font changes so he doesn't see them when composing. It doesn't have any effect on the fonts embedded into the message he's writing. But that will set the font displayed to the sender as he composes his message.