I have found the answer.
It is both yes and no :/
Through
This Thread and
This .PDF, I have found that a passive DP=>DVI adapter can be used only if you have two or less displays connected.
As soon as you connect a third display you must use an active DP=>DVI adapter.
It seems that, unlike DVI or HDMI, DisplayPort does not have a separate clocking signal, instead it embeds the clocking signal into the data signal.
Apparently, however, a DisplayPort connection is capable of passing the complete DVI or HDMI signal through it.
Therefore, as long as a DVI port is not in use, the clocking signal can be generated and passed through the DP connection, requiring only a passive adapter.
Once all DVI ports are in use, the card is incapable of creating any more DVI clocking signals and an active adapter must be used to convert the DP signal to DVI.
The video signal is not compatible with DVI or HDMI, but a DisplayPort connector can pass these signals through. While DVI and HDMI require separate clock signals, DisplayPort embeds the clock in the data signal.
DisplayPort Wiki Page
So, unless the OP has a monitor with a DisplayPort connection, I withdraw my previous recommendation and ask the OP to post his current hardware and budget.