Put simply: No. You can't have shots look the same through a spherical lens as they will on an anamorphic.
Anamorphics have their unique characteristics like their flares, but also oval bokeh, something you won't get from a spherical lens.
On top of that, anamorphic lenses have essentially the characteristics of two lenses - a 50mm anamorphic will have a vertical angle of 50mm, but a horizontal angle of 25mm.
This also means you'll find you'll have the DOF of a 50mm lens, even though the horizontal angle is as wide as you'd normally get from a 25mm.
So, yes you are correct. Trying to match an anamorphic focal length with a spherical lens will change the perspective dramatically.
Essentially, no you cannot have the image look identical between an anamorphic and spherical simply by cropping the spherical lens' image. However, many can't tell the difference. If you're simply looking for the bars on top and bottom, shoot with spherical lenses. If you really want the anamorphic look (and it is a look, much moreso than just extra bars on the top and bottom), then go for an anamorphic lens.