I had a gum graft on my lower gum (this is where they put new tissue to replace receding gums) and the next day I had my gallbladder removed (laparoscopically). This was when I was about 40. I had no real restriction on running due to the oral surgery, that I recall. The gallbladder surgeon said I could start running after 7 days, and I was on the treadmill that day.
I've had previous oral surgeries (major wisdom tooth removal, root canal), but all prior to when I started running. I did return to tennis pretty much the next day or two with those.
Hope the oral surgery goes well! I have a total phobia for that sort of thing, so mine was all done with a sedation dentist.