There will be no limitations at all other than the fact the new SATA III drive will not be able to hit the tops speeds it might be capable of if it were installed in a newer Mac that had a SATA III connection.
SATA II can hit 300 MB/s vs. 600 MB/s with SATA III. Take a look at the SATA III speed tests charts in
this test. Notice how the smaller file read/write speeds in those top couple charts don't hit 300 MB/s anyway, and much of the normal app and file use on your Mac is likely those smaller files. Not until you start moving to those lower charts with sequential reads of larger files do the SATA III speeds really start to matter.
Just in normal use with opening documents and launching apps, you would not likely notice much of a difference going from a SATA II to a SATA III Mac with an SSD. Now if you are working with 15GB videos or Photoshop files, then you would notice some difference.
Much of the big benefit of an in SSD normal usage comes from its very quick seek times and less so from its ability to do faster raw data transfers.
Does that answer your question?