Russia could be a natural ally of any nation trying to fight or defend against Islamic terrorist gangs. ( But America under Obama finsnces, arms, trains, defends, and promotes islamoNazi myrder gangs like PLO/Hamas, muslim Brothers, Iran , etc. All the worst and then some ) so - no alliance
Not for the length of time Russia has supported Islamic terrorism, even going back to Nasser. Their attitude seems to be that they will help the terrorists so long as they do not turn against Russia, as the Chechens did.
Putin is smart in many ways, but one of his weaknesses is his reflex adherence to old Soviet ways and alliances. That is his training, after all. It is all he ever knew, despite his nod to Solzhenitsyn's memory. In Putin's view, Arab states are clients, not headstrong equals as the Saudis view themselves.