Yes. Assuming that it is ethanol based (not the deadly isopropyl alcohol based) then the usual ones are about 120 proof. There have been case reports of kids (and some kids will ingest anything) getting alcohol toxic from drinking it. For a small child an ounce could be a very significant amount.
Most hand sanitizers are 63% Ethyl Alcohol. That is the same type of alcohol in normal alcoholic beverages, and is equivalent to a 126 proof drink.
However, the other ingredients in hand sanitizer make it unsafe to ingest in any quantity that would actually get you drunk… So, yes, you can get drunk, but you’ll probably get sick if you use it to get drunk off of.
Edit: Or what DSeid said…