Not sure the tree was Jesus although I can see a good allegory there.So, why would God block access to the Tree of Life if it was Jesus?
I'd say God blocked the tree so we (humans) would NOT live forever in a sinful state. Then, when we "eat" of Jesus now and become new born again creatures, I can see Him being THE tree of life and all who love Him will feast upon Him and His Words. JMO.
He is DE-VINE and we are de branches...abide, abide, abide...