Does the shortcut left on my Mac take up any space?

Practically none. A shortcut is a tiny record holding the location of the real item, so a multi-gigabyte folder leaves behind something measured in bytes. That's why moving gives you back almost the whole size of what you moved.

Two things can make the gain smaller than expected:

• Local snapshots. If your Mac keeps recent backup snapshots, the old copy can stay held for a while after the move. Storage Studio's What's Using Space shows this as Pinned space.
• New files. Anything saved into the original location after the move can stay on your built-in drive (see where new files go).

See Why deleting files doesn't always give the space back.