Not of itself. But if it is connected to your phone, the phone should pick up the change in time from the network operator, which will then transfer to the watch.
I thought mine had changed by itself in the past but not this morning. It was connected to my phone all night too. I got a GPS lock to update it but am disappointed it did not do it itself.Made me very confused when I woke and looked at the time. Lucky I looked at my phone which was next to me and realised my watch had not updated. What is the point of the tzmap downloads if it is not to provide timezone and DST information?
Furthermore, I just noticed my old F3 which is sitting on the side and not connected to anything is showing the correct time so the F3 changed automatically!
With the f5, I wonder if it's not that it needs to be connected to the phone, but a sync must occur. I believe a sync happens soon after midnight to finish off the previous day, but not sure if syncs occur other times at night, as there's really not much going on.
Now that I think about it, I'm not sure the last time I got a tzmap update on the f5. Often they come a bit before the start of DST shifts, as in some places the dates aren't consistent year to year. (disclaimer: I live in one of the places that doesn't do DST so I don't pay much attention to DST :) )
Mine didn't change by itself, did a Settings -> Time -> Time from GPS, and it adjusted itself, bit of a bummer, puts my watch on par with my oven, also doen't change by itself.
Mine changed after the first sync. Ok, but if you set an alarm this is not really what you expect, as I haven't yet figured out what is causing a sync.
I never know what to do with alarms when the clocks change - it's so variable which devices will update and which won't, and which will update the alarm too! My phone and bedside clock managed to update overnight correctly, but my watch didn't until I took the phone off 'airplane' mode and let Garmin Connect talk to it at which point it corrected itself.