I would say that it wasn't Google's design that beat Yahoo, it was the narrow focus on search. There is very little information to design on the Google home page and the expected interaction is incredibly simplistic, so designing the UI well should have been easy.
The problem is that most people see Google as a great example of engineers doing design, but there was really /nothing/ to design. If an engineer managed to screw a single search field up, then that's just bad. (And, I have known engineers who've screwed up simple search fields.)
My recommended guideline here: as information increases in density and interaction increases in complexity, the need to have someone focus on design increases. Now, is this person a bona fide designer or one of the engineers that has some design skill? That's for the individual startup to determine.
I would suggest that Google's design had a part to play in peoples preference in search engines. I agree Google's narrow focus on search was the defining outmaneuver. I would also suggest that this focus had to transcend their UI. The front page had to be a personification of their concentration on this function. It's subliminal and minimal but it's actually excellent design.
Although there is very little info to design on Google's homepage that is because that is how they designed it - clear, simple, plain, minimalist, yet colourful, memorable and vibrant. They could have had all sorts of ad's or other corporate info on there but they chose the letterbox and logo (which their 25yr old $100,000 a year designer changes on a daily basis so there is a lot of design going on by someone who is regarded as being one of the best apparently).
Google, to my mind, has a whole load of design. Just because you see white and primary colours doesn't mean there is no design. It's like talking, the worlds greatest orators were not masters of articulation and words...... but of silence. The most powerful and effective tool in speaking is the use of silence and pauses. When you deliver the killer bottom line when pitching your startup leave a long pause after. The last thing you said reverberates in the listeners head, over and over. I would suggest that Google's minimalist design does the same thing to users - they remember the brand and site because they never got LOST trying to FIND what they were looking for. I believe these two word are two of the most important to successful search functionality.
I had to outsource my design to someone who produced her best work on my site (Quarrysell.com - please don't laugh I'm new to this game, am a one man band and operate in a niche market). The advertisers I have lined up love my Google white minimalist design because my design (and Google's) does not detract from their logo, advertising and banners i.e. my main source of income (and Google's). Design is bloody important in building a brand and allowing users to easily navigate your site.
Although design is best incorporated at the beginning I do not agree that a designer is integral to hashing out a phase one project, this is not opinion but experience I sadly speak from. Design is a big deep hole of time, money and particularities startup have neither the time nor funds for. Good and excellent designers are obsessive about the smallest of things and this can hinder building the house.
My position: Once the foundations are solid, you have a roof over your head and windows to see out of then get the painters and decorators in.
The problem is that most people see Google as a great example of engineers doing design, but there was really /nothing/ to design. If an engineer managed to screw a single search field up, then that's just bad. (And, I have known engineers who've screwed up simple search fields.)
My recommended guideline here: as information increases in density and interaction increases in complexity, the need to have someone focus on design increases. Now, is this person a bona fide designer or one of the engineers that has some design skill? That's for the individual startup to determine.