Actually, I thought that while your Tamagotchi was on the Login Password screen it was effectively paused.
Here's an example of what I mean:
(1) the time is 9:00 AM, and you expect your Tamagotchi character will evolve at 10:00 AM.
(2) at 9:15 AM you go onto TamaTown for 5 minutes (leaving your Tamagotchi at the Login Password screen).
(3) at 10:00 AM nothing happens
(4) at 10:05 AM your Tamagotchi character evolves
However, this may be only for some certain models. I know for sure this is the case for the EnTama (the Japanese model that the V4 is based on.)
How you can tell for sure: hatch two V4 or V4.5 at the exact same time, and take good care of both. Go to TamaTown with only one of them. Do not go to TamaTown with the other. If they stay in sync; evolving at the exact same time, then going to TamaTown does not pause the V4 or V4.5