Arduino and Bluetooth USB dongle
No, the Arduino Uno can not use the Bluetooth dongle for two reasons:


To use an USB peripheral device such as the dongle, the Arduino would need to be a USB host mode, or USB OTG mode device. The Uno does not support host or OTG mode, though the Arduino Due and the Arduino ADK do. 
To support a Bluetooth dongle, you also need a "Bluetooth stack" on the host that supports a dongle. While there are some efforts out there to design such an open source stack for the Arduinos that support Host Mode, and possibly for "USB host shields", there isn't anything stable for USB dongles, that I know of, yet.




USB Host Shield:


(source)

Note that such shields usually do not have support for generic USB Bluetooth dongles. If there are some which do, a link would be interesting. 



Your other options are to either acquire one of those Arduino models that do support Host Mode, then experiment with the Bluetooth stacks available for it, or to use a Bluetooth module such as the Bluetooth Bee, or shields incorporating Bluetooth, and use those.

Serial Bluetooth Shield:

 (source)

The Bluetooth Bee:

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Requires a shield that supports the Zigbee type pin-out. Note that the Xbee pins are not the common 0.1 inch spacing, but a less common 1 mm spacing.

Shields that support ZigBee format modules:

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