Gall-Peters is definitely not conformal. It preserves area, but greatly distorts angles, apart from at the two standard parallels of 45 degrees north and south. This results in the shapes of land masses getting very squished towards the poles (and to a lesser extent, the equator). For an example, look at the shape of Greenland, which appears twice as wide (east-west) as it is tall (north-south), when in reality it's the other way around.

I'm also not aware of any of the main online maps changing projection as you zoom. It seems like that would be more pain than it's worth.