Yes, EAC includes it on writing.
The first pregap isn't contained in the image, so it doesn't
appear in your cuesheet either.
In fact, every pregap-lengh of Track 01 specified in a cuesheet,
will be added to the standard 2 seconds.
A first pregap of more than 3 seconds is violating the Read Book, btw.
Plextool's log seems to list this 2 second pregap, EAC doesn't.
That's why the difference occurs.