Yes, but I often don't try - though I have got it twice in GS so far. I find the presence of the Great Bath gives the AI something else to try for as well as HG and Stonehenge, so if you can start it early enough you have a decent shot at one of those last two.
As for the Great Bath, I haven't bothered trying for that yet as it goes so early, and ain't nobody got time to go for a wonder when you haven't even built the basic essentials yet.