it’s definitely possible. to most closely mimic what you’re describing i think you would want to make a browser extension that will search for certain styles and modify those styles on the fly. the class styles on the caption text in grid view in the Explore page are a little jumbled. so probably the easiest thing would be to set the entire caption class to {visibility: hidden}.
if you open up your browser’s developer tools, you could even do it there. it’s not a very automated approach, but once you added the visibility style, you could check/uncheck it to toggle the captions off/on, as needed:
sessilefielder made a Chrome extension back in the day that would change styles on the fly for another purpose, and it may help you understand what would be needed to go down that kind of path. see https://forum.inaturalist.org/t/computer-vision-should-tell-us-how-sure-it-is-of-its-suggestions/1230/44.
finally, i will note that there has been previous discussion in the forum about making standalone quiz games using iNat data, including at least 2 cases where folks made such games for folks to play. just search for the forum for “quiz”.