Is there any impact on watch battery life with Garmin Connect Mobile constantly running in background?

Maximizing battery usually comes at some sacrifice, so if you have access to charger... yes you would likely want to keep the automatic sync with GCM/phone enabled.  I would think that if you had it off, but had wifi setup for at home/office/etc that it would still get some updates when near your wifi areas.  If I go on a super long ride or ultra run, often i will turn off wifi (optical HR, screen dimmed, turn off some sensors that I am not using on activity, etc) on watch.  Probably all marginal gains of time... but better than watch dieing 10hrs into a run/ride.

NickMN said:

I would think that if you had it off, but had wifi setup for at home/office/etc that it would still get some updates when near your wifi areas. 

No, wi-fi sync with Connect only happens after an activity is completed (if auto wi-fi sync is enabled). It works this way because wi-fi syncing is more battery-intensive compared to bluetooth.

If you plug the watch into a power source, the watch will also use wi-fi to sync with your music provider (e.g. Spotify) if applicable.

Other than those 2 cases, wi-fi is not used by your watch unless you manually initiate a wi-fi sync.

NickMN said:

If I go on a super long ride or ultra run, often i will turn off wifi

No point in turning off wi-fi during an activity (or at all) imo bc of what I said above, but there's def battery gains to be had by disabling bluetooth.

When I go for a run, I almost never take my phone with me, so I always turn off bluetooth (as there's no point in leaving it enabled). If I forget to turn off bluetooth, the additional battery drain is noticeable.

Even the watch knows that bluetooth has significant battery impact. Rn I have 40% battery and my FR955 is estimating 7 days of battery life (general usage), with bluetooth turned off. If I turn on bluetooth, the estimate changes to 6 days.

in contrast, toggling wi-fi on and off has no impact on the battery life estimate.