Can bad wiring from a fuel pump mess up a battery and alternator

My fuel pump was replaced for recall in March. In April, my car shut off and would not start. I took it to my mechanic who tested the battery (it was just installed the day before) and the alternator with the diagnostic machine and checked the voltage. Both tested as fine. The diagnostic showed there was a problem with the fuel pump so I took it back to the shop that replaced it. They found the issue was the wiring had been done incorrectly and fixed it. I got my car back and within hours all the lights came on and then it stopped on me while driving. I had it towed back and the shop said it was the battery they tested it and it was not holding a charge. I took the battery to the store and they gave me a new one. The shop installed that battery and did a diagnostic to check for other problems. Everything tested fine. It broke down the same way the next day, now they are saying it is the battery and alternator. The test is showing both now. How are the fuel pump, alternator and battery connected? Could the bad wiring they did to the fuel pump have caused my battery and alternator to go bad?