I do sometimes. Usually I will hover over it with my mouse pointer, at least, just to see what it says and (if it’s a birthday) who the person is…
…but sometimes, if I don’t recognize the name (like today, I didn’t know who the person was), I will click on it just to see what made that person famous.
Learned something new today… the name of the person who first made the link between potatoes and lushes (put basically).
It’s the little graphic Google puts on their homepage for special events. Sometimes they animate or are interactive. There’s usually one or two per week*, though some are localised to specific countries.
Like the OP, I click on them occasionally for more info if it seems interesting. Maybe twice a year, though.
*Actually looks like they’re way more frequent now.
I never seem to remember that doing so will search for them. I’m more likely to see the name and google it.
Though I don’t see it very often, due to Google’s weird decision to make you click to see the Doodle if you have a theme on Chrome. And there’s no way to override that. If that wasn’t there, I’d see a lot more Doodles.