The scanner produces an image and saves it either in an image format or as PDF. Then you open the result in OCR software, such as ABBYY Fine Reader. You can also open it in Acrobat, as Acrobat itself has OCR components built in. If you were using Acrobat, you have a searchable document, unless Acrobat was unable to locate any readable character. Other OCR software may save a PDF, or another file format.
Another product has been mentioned in another answer; I don't know it, but it might be worthwhile having a look at it.
For the second question:
a) There is an Acrobat JavaScript Doc object method getPageNumWords(); if this methods returns a number greater than 0, the page you passed as argument has searchable text. You find more information about this method in the Acrobat JavaScript documentation, which is part of the Acrobat SDK, downloadable from the Adobe website.
b) There is a preflight check which finds out whether the page/document has Text objects. If so, it has searchable text. You will need Acrobat Pro, for this, however.