Putin and the SVR may try to wack him.
It's possible Putin might have known about Agca, and the plot to unseat the Pope, but based on my research, and thus knowing generally where and when he served in the KGB, I have a hard time believing it. Therefore, I don't think Putin would be out to knock Agca off.
The SVR might--as it was formed out of the First Chief Directorate, but if they whacked him, the Russians would find themselves in a diplomatic nightmare with not just the CIS states that border the Middle East proper, but the international community.
I also note that my observations on the current events in Moscow enable me to conclude that the Russians' economic and democratic reforms are contingent on Russian success with international relations--when things go in the crapper overseas for Russia, things take a crap domestically as well.
Basically, it boils down to this: Russia tries to whack this Agca guy, and they're up the creek without a paddle. It's the classic suicide move all around, at least as far as Russia's concerned. Putin's career will be destroyed, and the government will have another convulsion, making an already wobbly Russian democracy all the more unstable.