I don't think the issue is whether or not it is possible to win with a small budget. The issue, as I see it, is the hording of premier talent. When the O's opened up the purse in the late 90's some of their signings turned out to be mistakes, and they paid the price for it in the standings. The Yankees have made some mistakes with FA signings too lately, but they weren't held to that mistake because they just filled the roster spot with more premier talent -- acquired solely because they are the only team with the means to have $40M+ on the bench/DL.
Smaller market teams are at a huge disadvantage because they are unable to keep their premier talent -- they just can't match the offer of the big clubs. This puts a lot of pressure on their ability to scout and develop talent, and they have to do it substantially better than the big clubs in order to compete. On top of that, some of the best talent pools are found outside this country, and there is no draft for international FAs, meaning the bigger market clubs can sign the best and brightest stars in that market as well.
While baseball is a business, in the end it is a sport. Sports are governed and defined by fair play. Only a great fool would call the current system fair or equitable. My team benefits from the system, but that doesn't make me feel any better about it. Baseball, as a sport, is a bit of a farce until it eventually fixes this.
Oh, and don't mention revenue sharing. The Yankees are the biggest contributors to the revenue sharing pool, and they aren't liable for it for the next 4-5 years since they broke ground on their new stadium -- they are exempt while it is being built.