There are lots of mixed answers on the web if you search this question about Norovirus and Hand Sanitiser Gel.
Many sources say "no"; including many government health bodies like FDA and CDC.
Is that all there is to it?The answer is; no, it's not as straight forward as that.
It is clear that Sanitising Gel should not be used instead of washing hands as the removing of Norovirus from your hands needs the friction of hand washing to remove the soil that contains the virus.
That said, ruling out the use of Hand Sanitising Gel would be a bad move, because this gives you the chance to add in some extra points of hand sanitising where it would not be practical to have a proper hand wash facility, like in a school dining hall of instance or the entry point to a school or a medical facility.
Not all Hand Sanitisers are equal
If you are considering using a hand sanitiser, make sure you use one that has been tested as effective against Norovirus. The standard EN 14476 is the standard you need to see on the container and preferably some proof that it has been tested as effective on this virus specifically.