Does non-X Linux have a clipboard

Zsh doesn't support anything but internal registers, and bash doesn't support register at all as far as I know. By and large, shells support vi commands, not vim commands.

In zsh, here's a proof-of-concept for accessing the X selection from command mode. For real use you'd want to elaborate on these techniques. I use the xsel program, you can use xclip instead; see How to copy from one vim instance to another using registers. You'll find the features I used in the zle manual.

vi-append-x-selection () { RBUFFER=$(xsel -o -p </dev/null)$RBUFFER; }
zle -N vi-append-x-selection
bindkey -a '^X' vi-append-x-selection
vi-yank-x-selection () { print -rn -- $CUTBUFFER | xsel -i -p; }
zle -N vi-yank-x-selection
bindkey -a '^Y' vi-yank-x-selection

The function vi-append-x-selection inserts the current X selection after the cursor (similar to p or P). The function vi-yank-x-selection copies the last killed or yanked text to the X selection. zle -N declares the functions as zle widgets (i.e. edition commands). bindkey -a sets bindings for vi command mode.

Yes, basically, you'd need to offer the CLIPBOARD selection either as

• text/uri-list with the content being

  /path/to/file1
  /path/to/file2
  

• application/x-kde-cutselection or x-special/gnome-copied-files with content copy\nfile://$path1\nfile://$path2\0 or cut\nfile://$path1\nfile://$path2...\0

With xclip you can achieve this with something like

find "$PWD" -name "*.pdf"| xclip -i -selection clipboard -t text/uri-list

I've also found this loliclip command that looked promising, but though I could retrieve the values, I wasn't able to store them and have them retrieved from loliclip by pcmanfm successfully.

You also should be able to implement it in a few lines of perl-tk.