If it is anything like the reactor at UMCP (which it looks a lot like; open pool at the top of a tall concrete tower), they will be safe as long as they don't swim down to the bottom of the pool (20 feet down).
First, the reactor would be shut down; you don't operate it without people there, and idiots swimming in your reactor pool would qualify for a shut-down condition (if not the security breach, which, by the way, should have the cops there with weapons drawn.) The fuel rods may be dangerous to handle if fully exposed, but safe under all that water.
Second, the water is clean. Cleaner than bottled water clean. So clean that by having people swim in it, your instruments would probably detect the impurities added to the water. (clean water is very difficult to irradiate; impurities are easy; so you keep the water clean. You monitor the water because a small hole in a fuel rod would show up first as impurities in the water.)
When the UMCP reactor is operating at full power (250 KW thermal) there is a measurable dose at the top of the pool; I don't remember exactly, but on the order of 5 milli-REM/Hour. Low enough that you can go up there and see the pretty blue glow, high enough that you shouldn't linger there without good reason.
If this were to happen at UMCP, I think we would have a major security audit from the NRC, (and the state of MD), and we would have to run the de-ionizer on the water for a while to bring it back up to standards. Oh, and paperwork.
BTW, my knowledge is at least 15 years old, and I am not sure I had the details right back then. So, please, don't take my advice seriously. And don't go skinny dipping in a research reactor; it would mean a lot of work for some poor schmuck.