LiveTrack updates through your cell service to the Garmin computer servers, which push out the updates to whoever gets your LiveTrack. So it depends on how much connecting to your cell service drains your battery - if your phone is having to continually search for cell service, then it may drain it quickly. At any rate, thinking about it as searching for cell service may help you decide.
If you start your LiveTrack somewhere where you don't currently have cell service, it won't start until you enter an area with sufficient cell signal. Similarly, if you leave an area with cell service, your LiveTrack will stop updating. I've had my husband comment on both cases (he's the only one who gets my LiveTrack). If I start the LiveTrack without cell service, then the track will magically start appearing whenever I move into cell service. If I leave an area with cell service, then my track will just stop cold wherever I lost signal.
If your Garmin doesn't have cell service on its own (that is, it just connects to your phone via Bluetooth, and then your phone handles the cell service), then the Garmin battery shouldn't have any problem with LiveTrack - it would just be part of the normal operation of the watch to connect regularly to the phone. I mention this because some Garmins (I don't think the VA 4) have LTE and can actually make cell calls, etc., on their own without a phone.
Personally, I've used LiveTrack for some 10 hours without a problem, but that's obviously going to depend on individual phone batteries.