As the HOTAS has its own bindings, the answer should be No. There are three binding sets in the menu, two for the DS4 and one for the HOTAS, making changes to one shouldn't cause any changes to the other two.
Just a little side note, It makes a difference but in the ps4 setting one can atler the buttons. If one has done so, prior to playing make sure the check mark is unchecked. One doesn't have to change the settings to normal, just uncheck the box if you have changed any of the button via the ps4 settings. If for example one has reassigned a "X" to an "R1" for whatever reason, when ED fires up, and one deceides to use its setting to change the "x" again, the control will have a tissy fit, tring to figure out which of the two settings it's supposed to utilize as something else. When switching games, remember to go into ps4 setting and insert the check mark giving the control new commands.
ALWAYS start what ever game your playing with the controler you plan to utilize first. When I start ED, my hotas and ds4 are both plugged in, I start the game with my hotas, the ds4 capabilities are reduced to the scratch pad, and ear phone and if you have it, the text attachment for the ds4. Though I don't use the ds4 at all, so I have it shut off and removed.