To the website? No. To Google? Almost certainly given how it works.

I can imagine that, if Google already knows enough about you, just clicking "I'm not a bot" would be enough. Though I wouldn't know.

It seems like another way to punish people for caring about privacy.

There’s also this to consider: Google knowing enough about you to know you’re a human, and then wanting to use you to train. That’s why in some cases you can get away with just spamming whatever the hell you want in the picture grid. Because it trusts you enough to train it.