Not quite as the cropped portion is enlarged to match the size of the original. My example has the cropped portion enlarged to match the original.
Think of shooting 8x10, 4x5, 6x7, 35mm, and m4/3. Put a 150mm lens on all of them. Take a picture from the same point and then print all the images out on 11x14. I am pretty sure you are not going to think the perspective is the same across the formats.
However, it you shoot with those formats with a normal lens--300mm, 150mm, 90mm, 43mm, and 21mm. And then printed them out on 11x14, they would appear to have the same linear perspective.
There is more to linear perspective than just object distance.