It looks like it. I did a quick test, setting my system time several hours ahead. After refreshing the page, the options in the timer respected my system’s new timezone. I set the timer for a date/time 3 minutes ahead of my current (manually changed) system time. When I switched back to my real timezone, the timer was correctly showing 3 minutes until expiring.
Feel free to experiment and see if you get the results you are looking for!