putting locks on equilizer brand hitch

If you're talking about replacing the cotter pins with small padlocks I think it will be fine. All the cotter pins do is keep the pins from vibrating out of the hole.
The only downside I see is the fatter locks possibly contacting another part of the hitch if you turn tight. But you can check this by putting the bars in and locking the pins without a trailer attached. Then just swing the bars by hand and see if they hit anything.