Usually you can get close, but not perfectly preserve it. A printed photo is already a reproduction: ink or dye is laid down as patterns of dots or grain on paper, while a scan records that print as pixels. Converting from print dots/grain to scanner pixels introduces some loss and can also create artifacts.

In theory, if the scanner samples at a high enough resolution relative to the print detail, it can capture nearly all the information present in the print. In practice, scanner optics, sensor design, internal processing, paper texture, print technology, and color reproduction all limit the result.

So the best answer is: a scan can make a very good copy of a print, especially if scanned at sufficiently high resolution, but it will only be an approximation of the print, not a perfect recovery of the original source image. There is always some generational loss in a print-to-scan-to-print workflow.

If the print and scanner quality are both high, that loss may be very small. If either is low, the loss can be obvious.