I’m looking at a 2006 Boxster S with a replacement motor done by Porsche in 2008

I have the serial number on both engines, but no other information

Is it possible to tell if it’s a non-IMS engine by the serial number?

 

The type MA1 engines (model year 2009 and later here in the USA) have no intermediate shaft at all. If your car got an M96 or M97 engine, then it does have the shaft and a (possibly) troublesome bearing.

If you scroll to near the bottom of this Wikipedia page, you'll find serial number ranges for various Boxster engines.

 

Post the new engine number. Most likely it has the last version of the IMS. The engines from ‘09 also have different, non-interchangeable engine management systems.
Factory warranty replacements would have replaced ‘like for like’.
If the engine number is stamped with ‘AT’, that designates factory replacement.

 

MY06 from engine No. 62504095 onwards is known to be the ones which Porsche fixed before they moved to the 3.4 lump

 

All replacement M96 and M97 engines will have an IMS shaft. To clarify, the MY06 and later built engines will have the larger, non-serviceable 06-08 ims bearing.