I saw info stating that gog's client will not work with cross-play. But my question is that if I run the non-steam version of the steamcmd server, will that allow the gog client to connect for cross-play with steam clients that have the -nosteam option set?

I went ahead and tried this.
My non-steam server did allow both steam clients and non-steam(gog) clients to connect and cross-play.

Just wanted to provide an answer for anyone else that may be wondering the same.