Is it permissible in Sharia to collect Zakat funds for three or four years in an Islamic bank account to establish a non-profit da'wah center, and then later inject the annual Zakat into the center's operations?

It is not permissible to delay the distribution of Zakat after it becomes due, except for a legitimate Shar'i excuse. It must be distributed immediately. It is not permissible to trade with Zakat funds or invest them, whether by the one on whom it is obligatory or by institutions, because it is obligatory to spend it in its legitimate channels as stipulated in the Quran. It is not valid to spend it in other than these channels, such as building hospitals or charitable projects.