Yes, and it clearly shows that they had not eaten of the tree of life, as eating once makes you immortal; thus the man can’t be allowed to reach out his hand, once.
This is peripheral to your main point, of course. I wasn’t disagreeing with that at all. In fact it supports your point; Adam was mortal, not yet having eaten from the tree of life. One must also suppose there was real, not just potential, death in the garden if there was even a single annual plant in it, at the least, not to mention all the insects, worms, and such with short generations. We must posit either death or birth control if we are to avoid being buried in flies.