[nitemice]

No, tmux-yank only does the copying part.

To get pasting from the system clipboard, you need something like https://github.com/brennanfee/tmux-paste It will copy whatever's on the system clipboard into tmux's paste buffer, and paste it, all with a single middle-click.

I've only recently started using tmux, and all this clipboard stuff was the biggest stumbling block. But I think I've got things work well enough now.