Sort of... the Bitvise SSH client I use for tunneling, it comes out of box understanding that Pageant is an available agent and will reference it; a lot of tools know that PuTTY is common and therefore expect the tools to be present.

With git and tools that use Git, PuTTY distributes plink.exe, which acts as a helper. So you set something like...

  GIT_SSH=c:\Program Files\Putty\plink.exe

To make that happen. So PuTTY is not my shell, but is still pretty important for its good set of overall tools.