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Yes, you absolutely need to be concerned. Toyota themselves specify that a Matrix must NOT be flat towed with the automatic.
That's the same as coasting with the engine off. Don't do it.
Back in the day the manufacturers figured out that they could build the transmissions with only the front fluid pump, as the rear one was superfluous; as long as the engine was running the front pump was turning, providing fluid throughout the entire transmission. The rear pump, attached to the output end of the transmission, was unneeded (IIRC Ford was the last company to include the rear pump as a matter of practice, so it was still possible to push-start auto-equipped Fords for a while).
Rolling short distances at low speeds is one thing, but coasting at speed will destroy your tranny.
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Lead or follow. Either is fine.
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