I have actually witnessed it first hand. When I have a budget for advertising, I tend to use it up quickly; but when I don't, I spend a lot of time thinking of ideas to get free promotion in other ways. Lack of resources does push you to be more innovative. The only downside is if you find your fundded competitor spending on marketing and getting all the buzz and attention while no one ever talks about you.

"It would create a false sense of security and breed complacency, both of which are more fatal to a start-up..."

Yes, this is true for anything. As soon as you get a few bucks, a good developer, a good idea, a great hack, or even a little help from an unexpected place, there is a natural tendency to "let up". Don't do it! These are the best times to really "turn it on", as if it's your only chance.