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You can't trade a player you just signed before June 15th, making sign-and-trade impossible without the players written consent. So it's technically possible but has it ever happened? Not that I can find.
But Smith was not a free agent. Picking up an option before trading a player...Lind came to us in such a situation, looks like it was only 6 days from pickup to trade. Zobrists option was picked up by TB in the offseason he was traded to Orcland. That happens without much fanfare so I'm finding it difficult criteria to search for.