Do I think it's possible? Absolutely. Do I think it you're reducing your chance of success without trying? Absolutely.
Coming from a marketing side I may be biased hence the upfront disclosure, though here are my thoughts from the many times I've encountered this debate. I've come across many of the more technical managers/execs who believe if you build good product customers will come and treat marketing as an expense, not an investment. I agree here to an extent for differentiated technical products being sold to technical people. Engineers like to evaluate and consider products closely. More information is better (to a point) when selling to technical people and sales department is likely a better area of investment. And while technical people may take this approach to everyday products, the mass don't.
Most people are not technical. If you are trying to sell product/service to the mass markets they typically buy what is 1) Placed in front of them , 2) At a perceived value price point 3) With brief & easy to understand core product messaging.
Form this, for the masses, good marketing can make or break a business. And remember marketing is more than a pretty website or some blinking banner ads. Marketing is many fields, one of the most important and least discussed being distribution. This is often given little attention and IMO a key component to get right. I would say typically a weaker product with great distribution has a better chance of success than a great product with weaker distribution. Think ASUS vs Dell, VHS vs Beta Max, HD DVD vs Blue ray, IE vs Opera Browser etc.
All this aside, people simply need to track ROI and be open minded with marketing. I've been in the position of showing a shrinking department a marketing test that a $1.00 spent on tested activities will return $1.30 in profit. Some technical execs stopped further spend going forward being stern holders to the build a better product and people will come thinking, and marketing is some cheap trick they are better than. It is just stupid rigid thinking. End of the day do some testing with various marketing channels. If your marketing efforts whatever they be can produce more profit than spend, do it. If the tests cannot show any results, then close down this as any bad investment. Overall, given the plethora of success you see with advertising, anyone would be a fool for not actually trying and basing their decision on philosophy vs fact.