Would depend on the specific recipe I suppose but for all practical purpose - no it can't be canned.

Most recipes for it contain lots of butter and dairy fat (cream). Neither are usually allowed in canning since it insulates the bacteria and prevents the heat from killing it. Then there is the density issue. It is usually so thick that it would take a fair amount of time for safe heat penetration. Lastly, the pH. It is entirely made from very alkaline ingredients with no added acid. That alone means it could not be home canned except in a pressure canner.

Dave

What about syrup that is just sugar and water? Would that make any difference?

Alkaline, even low acid, foods require pressure canning and water is very alkaline. Adding sugar to it has no effect on the pH and adds no safety.

So in theory, if you wanted to can sugar water it would have to be pressure canned but the lengths of time required has never been calculated. In theory, 25 to 35 mins would be long enough but that is just a guesstimate.

Dave