Can this program convert my Microsoft Works .wps documents into Microsoft Office for Mac?

Convert .wps to .doc for Mac

Probably not too reliably. LibreOffice’s main concern is the reliability of the ODF file format.

I think the most appropriate tool for that is probably MS Office for Mac.

For MS Works for MacOS text / spreadsheet / drawing / database documents the MWAW filter evidently does a good job (as indicated in this question). For Windows MS Works files there is currently poor support.

Normally, the support for Windows wps has been greatly improved in the latest versions of LibreOffice, so it must now be a lot much better than one year ago. In LibreOffice 4.3, some small support for wdb/wks Microsoft Works v1-v4.5 Windows will be also added…

Concerning the Mac wps files, LibreOffice must do a good job for v1-v2 files ; for the other formats/versions, you must try (i.e. I have only few files to test, so some problem can remain :-~ ).