Placed PSD file and honour blending mode from PSD file

This problem has existed for over 2 decades now. Strangely Corel Draw was able to accomplish  that last time I checked.

You will need to make 2 PSD files, one with shadow only (assuming that from your post as that is #1 reason by far to do that)  and the other with the color art. You can then set the filename_shad.psd to multiply in Illustrator, and place a copy on top of the color field in normal. 

FYI I set the shadow layer viability off in the color file, just so I do not misplace/lose that as illustrating perfect shadows can be time consuming. You can use the drop shadow effect in Illustrator as the shadows are ok, but not as realistic as a hadndrawn one with a hard and soft shadow/persepctive/etc.

The long answer is no.

When you embed the image and make Objects out of layers, then you can set it to Multiply again.