The latter two potentially yes, as they can sell a product. Chrome - not so much: sell the browser, embed ads… nothing palatable.

> Would Chrome, Android, and YouTube be viable companies without the money-printing engine that is Google’s ad business?

Short answer? Yes. Long answer? Definitely.

> I wonder whether a good balance could be struck between great services like these versus how they actually make money.

I see you have an unconventional definition of the word "great". I'll take that to mean you're an outside-the-box thinker, so you're in a good position to understand that a break up of Google would radically change all the markets they're dominant in.

If Android 'dies' post-breakup, that would leave a gaping hole in the economy. iOS might fill it, but regulators would need to break them up too. Say iOS 'dies' too, would we all collectively just stop using smartphones? Obviously not. Entrepreneurs who can see opportunity will raise money and hire the right people to build a new OS, foundations will apply for grants to maintain Android or iOS forks, industry standards will form to improve interop and reduce development costs, etc. The sky's the limit!