hello, Unless the cabinets are really in rough shape they should be fine, we
just did a reface with old 5/8 melemine cabinets sides set 1 1/4 stone on top
and all is fine.

screw the wall into the floor ...in floor joists if possible....and yes attach
wall to cabinets...if the island is attached to the floor then you should be
fine.
Ralphw