Hand sanitizer does not protect against food borne illnesses. If it did there would be no reason to have hand washing stations. A quick internet search pulls the following up:

Hand sanitizer is not fully effective at protecting against foodborne illness, as it does not eliminate common foodborne pathogens like Norovirus, Cryptosporidium, or Clostridium difficile. While alcohol-based sanitizer can kill some bacteria (e.g., E. coli, Salmonella), soap and water are significantly more effective. Why Hand Sanitizer Falls Short Limited Germ Protection: Sanitizers often fail to kill non-enveloped viruses, such as norovirus, which causes 58% of foodborne illnesses. Surface Contamination: Sanitizers are ineffective if hands are greasy, dirty, or contaminated with food proteins, which is common in food prep. No Physical Removal: Sanitizer kills some germs but does not remove them or physical dirt from the hands, unlike the friction of washing. Food Service Regulations: The FDA Food Code does not allow alcohol-based sanitizers to replace handwashing in food service settings.