Can an APFS-formatted external HDD successfully transfer Word 2011 files from iMac 10.6.8 to iMac 10.13?

A machine running Snow Leopard won't be able to copy any Word files from a machine running Snow Leopard onto any of the APFS volumes. Apple didn't introduce APFS until Sierra 10.12.4 (in a limited, experimental way) and High Sierra (for real).

You might be able to partition a drive, using most of it for APFS and part of it for HFS+. But that seems a bit on the complicated side. If this is a hard drive (not a SSD) being used just for data storage (not as a startup drive), you might just want to format the whole thing as HFS+ and leave it that way.

@Servant of Cats is correct.

Why not just enable File Sharing on the older Mac and allow the newer Mac to connect to the older Mac so the files can be transferred over the network?

While this Apple article is referencing macOS 10.13 High Sierra for enabling File Sharing, I don't believe it was too much different even with the older versions of macOS like 10.6:

Use file sharing on Mac - Apple Support

That should be fine. If for some reason 10.6.8 will not copy to the drive that is running 10.13, then reformat the Mercury Elite Pro to Mac OS Extended (Journaled) and then copy from 10.6.8 to the drive with the system running 10.13.