yes it can eventually. i have installed that harness the 70-5519 one on plenty of mustangs and have yet to have a problem but the harness you showed me off crutchfield will work too, its just about 3x as expensive
What I did was buy a ford premium sound harness(they have this at wal mart or any car stereo shop) which includes the 1st and 3rd harness shown in the attached picture. You need to have a head unit with at least 2 pairs or preouts, 3 if you want to add a sub. Splice/solder some RCA's plugs on the "3rd harness in the picture" connect them to your front and rear preouts and Voila. This way you use the clean preout signal, not your distorted amplified signal into your mach amps. Higher preout voltage seems to work better also. It is a very simple install, the hardest part is soldering the the rca plugs to the harness since the wires are kind of small. I will post pics if I ever have to tear into my headunit again.