Yes, of course... but in a "proper" GMT, the fourth hand says steady while the main hands are moved.
In theory, this enables you to cange the main hands to local time, whilst leaving "home time" where it is.
In reality, few of us spend so much travelling to make this a worthwhile complication....
I travel a bit. China, Japan, Taiwan, etc, perhaps three times a year.
I find a GMT watch really useful. I keep the fourth hand on China time when I am in the UK. When I'm travelling, I ajust the main hands to local time, and the fourth hand to UK time.
OK... its a bit of a fiddle. But it is a 12 hour flight from Heathrow to Hong Kong... 12 very boring hours.
I need somethin to occupy my mind.
Ajusting a real GMT would take a matter of seconds. (Although I would stil have to fiddle around, for a minute or two, changing the fourth hand to home time)
Ajusting my "improper" GMT replica watch wastes four or five minutes....
Sometimes I fill up the flight time by taking two watches with me.