Yes, but that has nothing to do with conversion. From the start pagan factions are able to build both christian and pagan shrines, it has nothing to do with conversion. For example start with the pagan Alemanni. Destroy the pagan shrine and then you have the option to either start a pagan or christian temple.
It does.

When you build the christian temple you convert the offical religion of the city to christainisty. Then when you build a church it opens up a new part of the tech tree.

Therefore conversion opens up a new part of the tech tree.