Yes and No.
Yes: the sun and moon positions are shown correctly, such that you can see the moon pass the sun.
No: the lighting on the ground and in the sky resulting from the eclipse is not simulated at this time.
Here are some screenshots showing what you can expect for the Aug 21 2017 eclipse, as seen from Casper Wyoming:
So far, so good, but the lighting on the terrain is not affected by the eclipse - it's as if the sun were not actually blocked by the moon:
One other thing the app does do currently: the relative size of sun and moon are shown accurately. That means that an annular solar eclipse (where the moon passes in front of the sun, but is slightly too far from Earth to cover the sun completely) can be viewed in TPE 3D. Here's an example - Dec 26 2019 from northern Sri Lanka:
We hope to offer realistic eclipse lighting conditions in a future update (but it's a tricky problem!)