For example:
* The major mode should usually have its own keymap, which is used
as the local keymap in all buffers in that mode. The major mode
command should call `use-local-map' to install this local map.
*Note Active Keymaps::, for more information.
This keymap should be stored permanently in a global variable named
`MODENAME-mode-map'. Normally the library that defines the mode
sets this variable.
So you could check (keymapp (intern-soft (concat mode "-map"))) in the
apropos-internal PREDICATE.