Yes, both.
See the help for supported fields:
If you are asked for a field name, enter the name without the % around it.
If you want to address the contents of a field with a field variable, then the % is mandatory.
To copy the contents of an existing field to a new field, use (as you did) an action of the type "Format value" and enter as field name the name of the new field (here: SYLT).
Enter as format string and instruction to generate a string - which would be the contents of the %unsyncedlyrics%. The field LYRICS is a user-defined field, I think - to see the proper name, open the extended tags dialogue (Alt-T) and check the field name.
If you enter SYLT as target field then you create a user-defined field called SYLT which appears as TEXT field in the tag. A player will probably not recognize this as the standard SYLT field.
See also this thread: