Can you explain in more detail the why/what/how of your enquiry?
Are you asking about a file that has been written to disk? How to check if a saved TIFF file includes this “transparency” information? If so, you may have better success posting in the Adobe Bridge or Adobe Bridge Scripting forums.
I can find differences between a file with and without the “save transparency” option using ExifTool, however I am finding it harder to find differences using only Adobe tools. Somebody with scripting experience in Bridge can likely point you in the right direction in finding these alpha/transparency related metadata differences.
The ExifTool reported differences are (as expected) related to an extra “alpha channel” of info, such as there being an extra bits per sample count (8 8 8 8 vs. 8 8 8 for an RGB file), samples per pixel 4 vs 3, ExtraSamples: Associated Alpha, AlphaChannelsNames: Transparency.