Presuming that such tree exists and is found - certainly. If not, no.
Apologies, I don't get precisely what you are saying. (Also worth noting that ultimately I see 'free will' as an illusion hence I don't put any stock in it at all).
Assuming that 'free will' exists, (which by very definition negates external determinants), then Adam and Eve would be free to either eat the fruit from this tree that resided in the middle of the garden or free not to.
Of course free will doesn't work in reality and even if it did there are certain things a loving entity could do to lower the chances/ ensure the safety of his loved ones. In this instance, removing the snake is part of such entities responsibility - we would never admire or condone it if a human did it and I have yet to hear any valid justification for a god allowing his presence. Secondly, this god could have made the fruit rotten looking - with mould and maggots. That might have been enough to ensure they did not eat it. Neither of these - in the theist world - negate 'free will', (they could still freely choose to eat it even if it was maggot infested and rotten).
The A&E story is of course utterly ridiculous - even as fiction, but without it being factual, christianity falls apart and Jesus' supposed existence is left without sufficient explanation.