I've OP'd many times on less than an empty stomach and didn't notice any problems. I do think you get more benefit on a semi-empty stomach, probably two hours after your last meal.
I used to regularly pull at night with coconut oil when I found out it helped me sleep. I'd always try to do it a couple hours after eating. Be careful though, because any other oil I tried pulling with was energizing and kept me awake into the wee hours.