Not even close. Afghanistan led by Taliban is a threat that must be closely monitored. The Wahabi threat along the border as a legacy of western presence in Afghanistan can be a common ground for cooperation with Taliban but it cannot be a reason to claim Afghanistan is a natural ally of Iran.
Saying that Afghanistan is a natural ally of Iran, is an over statement. Taliban has deep contradicting and in some cases conflicting ideology with Iranian one. Yes there maybe cooperation with Afghans regarding threats that threatens both but still your statement is exaggeration.
If you said that about Pakistan, i could give it a chance. Still Iran-Pakistan relationship is badly influenced by Saudi shadow and western pressure on Pakistan which forces Pakistanis to consider balancing measures.
But all in all, Pakistan is more civilized, more disciplined compared to Afghanistan.