I don't think so. If it's that stretched by tides, then the world's going to be torn to shreds.
That said, the E atm description in bOok 6 is just plain silly anyway. It says "the world's surface is ellipsoidal, not spherical in shape. Because the atmosphere remains spherical, surface atmospheric pressure ranges from very high at the middle to very low at the ends. Breathable bands may exist at some point within the range of pressure".
See the problem? It claims that the solid, rocky, non-responsive surface is ellipsoidal, but the fluid, responsive atmosphere is spherical! But tides will, if anything vastly affect the atmosphere and ocean much more than the solid body, so it should be the other way round - the atmosphere is ellipsoidal and the surface is spherical. Besides, I can't think of any way that the surface could be so distorted without the atmosphere also being distorted.
Now, it
might be possible for the atmosphere to be distorted by tides and the surface to be effectively spherical. Look at somewhere like Titan - the tidal bulge raised there by Saturn is on the order of 100 metres - it's probably a bit more in the atmosphere because that can respond more easily. If the orbit was circular, then this bulge would stay in the same place relative to Saturn in both the solid body and the atmosphere. But the orbit is eccentric, which means that the bulge moves relative to Saturn so the thicker part of the atmosphere "wobbles" over the equatorial regions. But of course the pressure difference between the poles and equator because of the bulge isn't so large as to change it's atmosphere type.
There's an example in vol 2 of the the awesome
2001 Nights manga comic trilogy of a world orbiting Algol that suffers from horrendous tides. I don't think it's particularly realistic, but the stellar tides basically pull the atmosphere so much that pretty much all the air rushes from the poles towards the equator during an orbital cycle. The three expeditions that go visit end up getting crushed by huge boulders blasted around by the winds at the equator, drowned in tidal waves of
sand moved by the wind in a desert at midlatitudes, and nearly killed at the poles when they're frozen to the ground as the air pressure drops at they end up in a perfect vacuum there. Perhaps that kind of thing might be more what a Type E should be like... (it's probably not much more realistic than the default, but it's cooler IMO
)