They made it pretty clear in their IFA 2014 press conference that it was "fully future proof" and the slide specifically mentions "Bluetooth & Wi-Fi" (I can't link the video...)
I have seen multiple articles, as well as the LG UK tweet that seems to confirm that that it doesn't - but the tweet might be wrong (or refer to the square G Watch), and all the articles seem to cite either it or each other. That is to say, it's a lot of mutual speculation.
I have also heard that Wi-Fi should share the antenna with BT, though I'm not certain if that is true. Furthermore, they do have FCC certification for Wi-Fi.
Either way, the iFixit teardown makes it look relatively easy to pull apart, I wonder if it would be possible to add an antenna if it really doesn't have one. Surely the Wi-Fi function could be forcibly enabled with root, and we know the chip has the ability, it seems like the only issue would be soldering on an antenna.