I can assign F1 through F16 for paragraph styles, but pressing the corresponding key with a text cursor in a text frame has no effect. Assigning other shortcuts, say, Ctrl+Y, works as expected.
Tested with German keyboard layout on English language setting of Publisher, USB keyboard connected to MacBook. OS is 10.11.6 (El Capitan).
Curiously, pressing any F-keys hides the transform controls and frame/column outlines temporarily until the mouse pointer is moved.
If this has to do with certain F-keys being taken over by OS shortcuts like launching Dashboard etc., I would expect Publisher to check for that and display a corresponding warning when assigning the shortcut.