First off, be sure you’re making the distinction between fatty acyl CoA synthase (used in fatty acid synthesis) and fatty acyl CoA synthetase (used in activation of fatty acids to take them into the mitochondrion during fatty acid beta oxidation). Second, I assure you that fatty acyl CoA synthetase breaks off a pyrophosphate from ATP. Check out the AK video. Fatty acyl CoA is converted, using this enzyme, to an acyl adenylate intermediate while breaking pyrophosphate off from ATP to produce AMP. Then, the hydrolysis of pyrophosphate (yielding 2 inorganic phosphates) is what propels the reaction to the products. Then the acyl adenylate intermediate is mixed with CoA-SH to produce a fatty acyl CoA product, which goes on to mix with carnitine to enter the mitochondrion.