There are extensively documented records of entire meals being delivered through the media of chewing gum. One particularly famous and interesting development was a three course meal including tomato soup, roast beef, and blueberry pie for dessert. Though I seem to recall there was an issue with it during testing that prevented it going to mass market.
Is there some kind of protein-infused gum I don’t know about? 😂
The answer to your question is no. The only digestive enzymes in your mouth are primarily carbohydrate-related (salivary amylase), and to a lesser degree, lipid-related (lingual lipase).
In an amount that would actually matter? No. Think about the size of a typical piece of gum. Maybe 5-10g. It’s probably possible to create it in a way that you absorb some of what you’re chewing. But for it to actually be gum, most of it will not be swallowed, the majority of the mass stays in your mouth while chewing. So unless you actually swallow it, most of the protein, if there was any in it, would be still in the gum you eventually spit out.
And of course, consider that if there was a reasonable amount of protein in there, the consistency probably wouldn’t work to actually be gum anyway.
If you want quick easy ways to get in protein, protein gummies and powders are probably best.