Does cropping a 48MP image from 200mm match a 24MP image shot at 400mm?

Your question seems to make a false assumption: That cropping a digital photo by 2X linear measurement will result in an image with half the pixels of the original. This is not the case. If we crop a digital image by half in both width and height, we end up with one-quarter the number of pixels we started with.

A 36x24 mm full frame sensor covers 864 mm². An 18x12 mm "half frame" sensor would cover 216 mm². If both sensors have the same pixel pitch, the "half frame" sensor would have one-fourth as many pixels.

To reduce the number of pixels by half, one would need to crop the linear measures of the image by the square root of two, or approximately 1.414X. A 36x24 mm sensor would have approximately twice the area of a 25.5x17 mm sensor. This is not too far off from the dimensions of APS-C cameras, which use sensors ranging from a 1.5X to 1.6X crop factor and measure from around just under 24x16 mm to around 22.5x15 mm.

If you cropped an image taken with a 48 MP camera and a 200mm lens by 1.414X it would result with an image that is 24 MP and had the same field of view as a 285mm or so lens using the full 48 MP sensor. To get the same field of view that one would get using a 400mm lens on the full 48 MP sensor, one would need to crop 2X when using the 200mm lens. That would leave one with a 12 MP image containing the center quarter of the original area of the full sensor.

But you still wouldn't have the "same" image. To project the same amount of detail onto a sensor area half as tall and half as wide as the full 48 MP sensor, the 200mm lens would need to be twice as sharp, in terms of the number of line pairs per mm it could resolve, as the 400mm lens projecting the same field of view onto the full 48MP sensor! This is because when we view both images at the same display size, we are enlarging the cropped 12 MP image by twice the enlargement ratio that we would use to view the full 48 MP image at the same display size.¹ And we'd still have one-quarter the resolution in terms of megapixels.

¹ This is one reason Medium and Large Format cameras can give such sharp images with relative simple lens designs: the enlargement needed to get to a specific viewing size is much lower than that needed with a 36x24 mm or smaller image format. An 8x10 contact print of an 8x10 negative has an enlargement ratio of 1:1. An 8x10 print from a 135 format (35mm) negative must use an enlargement ratio of 8.47:1 to get an 8x10 print. All of the lens' imperfections and blur is magnified 8.47X by that same 8.47X enlargement!