Kosta,
Some time ago, I wondered the same thing. So, I decided to conduct a simple experiment in which I used a small amount of a natural starter/preferment directly out of the refrigerator. The starter was an active starter, that is, it was regularly maintained, but just not at the time I decided to use it to make a pizza dough. In my case, I combined the starter with a small amount of flour and water (cold) to make a "prefermented dough" and allowed the prefermented dough to preferment overnight at room temperature before incorporating it into the final mix. I described the experiment I conducted at Reply 175 at
http://www.pizzamaking.com/forum/index.php/topic,576.msg12748.html#msg12748. If you read that post, you will see that the dough fermentation was very labored and it took several hours for the dough to develop, with little noticeable expansion. Surprisingly, however, the results were very good. I did not conduct an experiment using an unrefreshed starter in a dough formulation from the outset, that is, without the overnight prefermentation, but I believe the principle you mentioned would still apply. However, it may take forever for the dough to properly develop to the usable state. Maybe sometime you can conduct such an experiment to test out your "theory".
Peter