There is nothing built-in that will do this. 

If stored in the registry in a simple manner, a "Custom Data Form" could be setup to collect it.  Otherwise, one may need to run a script to extract the value to a place where a CDF could collect.  

For Office, there is a tool that ships with Offce "cscript ospp.vbs /dstatus" that returns the partial value....

Examle - Last 5 characters of installed product key: ESGGD

This result could be parsed to the registry to be collected.  It would not be the full key, but that may be better.  I would be enough for you to ID which key, without exposing the full value which is why MS likely did it this way.

One would perhaps tweak their VBS script to get the full value, but I did not look.