Run 'Remote SSH External Tool' as part of Connecting to a Remote Host?

I'm trying to compile a cmake project on a remote server, but my remote environment requires that I first run an interactive expect script to configure the environment. The expect script sets up the PATH, creates a fakechroot, and sets some other environment variables necessary for compilation. It stays running waiting on input so that you can CTRL-D out of it when you want to exit out of the development environment.

I've created a 'Remote SSH External Tool' which calls this expect script and it seems to work in the console (root, PATH, and environment variables seem correct). Would it be possible to call this Remote SSH External Tool immediately after connecting to my Remote Host Toolchain's SSH connection and prior to having it run any sanity checks on the environment? Currently just connecting to my remote host under Build, Execution, Deployment -> Toolchains it says CMake, C++ Compiler, and Debugger are not found as they're only added to the path after running the interactive expect script.

Thanks