The common-sense view: Yes!
However we better be careful about this issue. For example, we can ask: does culture matter in Olympic performance? Are some cultures more determined or hard-working than others? Are some cultures simply more "sports-minded"? As you can see, the culture-performance debate is not that simple.
Exhibit A: The historian Rodney Stark claims that the origins of modern capitalism can be traced to Christianity. He stands the usual argument on its head, that medieval faith was the scourge of the "Dark Ages". His argument: on the one hand, Christian theology is fundamentally committed to reason, the improvement of material conditions, and the autonomy of economic and spiritul life from the political. On the other, Christian monastic orders became the vanguards of commerce, and eventually, of capitalism.
Exhibit B: The Indian Economy blog takes umbrage at remarks made by renowned management guru Kenichi Ohmae. Essentially Ohmae is attributing the failure of Indian manufacturing (relative to say the spectular rise of Chinese manufacturing) to a cultural factors: Indians are "too inquisitive", limiting their ability to excel in disciplined factory-style work. Nay say the economists: Indian manufacturing has been stifled by state regulation; remove the regulation, and manufacturing would respond to economic fundamentals, such as the great degree of labor abundance in the Indian economy. Please read the comments, the ensuing debate is fascinating.
About the Philippines: we often read plenty of self-criticism about our poor teamwork, proclivity for petty politicking, "talangka" (crab) mentality, fondness for backstabbing, lack of punctuality, cunning dishonesty ("mahilig magpalusot"), and the thousand-and-one elements of a "damaged culture". And this is why we are so poor, and the rest of the world is getting rich.
I don't buy it. These are failings, for sure, but if you read newspaper columnists in virtually any country, there will be lots of cultural self-criticism being dished out. And similar name-calling and blaming for economic failure. This is all silly. There is no way to measure the importance of these cultural factors - if the stereotypes have any empirical value at all - in the economic performance of any country. I think Philippine culture has constrained economic growth, to the same extent that Philippine culture has prevented Filipinos from bagging an Olympic gold. Namely, not at all.
How to win an Olympic gold? Spend, spend, spend. Sponsor lots of competition. Get the average health and fitness level of the population up, to widen the pool of improvable talent from which to develop superior athletes. Import lots of foreign expertise to bring our techniques and training to world standard. Offer big monetary incentives to gold medalists. Hey, we seem to have started doing some of this in the recent Southeast Asian Games.
That sounds suspiciously like a prescription for economic excellence as well. Hmm...