Can these testers check the alternator and starter, not just the battery?

Yes, most of the digital units here (TOPDON BT100/BT200/BT600, FOXWELL BT705, ANCEL BA101) advertise charging-system and cranking-system tests in addition to a CCA battery health reading. According to verified-purchase reviewers, the alternator/cranking functions are a major reason buyers pick these over a simple voltmeter, though results are best treated as a quick screen rather than a definitive diagnosis.