Yes and no.  DVI-I connectors actually carry BOTH the Digital and Analog VGA signal.  That dongle removes the VGA signal from the cable and changes the connector to match a VGA port.  It does not convert betweent he two.  The main thing to look for to see if you can do this is the 4 pins around the flat bar'ish looking thing.  A straight DVI connector with only a digital signal will not have these, while a DVI-I connection will and will carry the analog signal on those 4 pins.

However if all you have is a digital signal, you will have to convert, which as already pointed out is a bit on the expensive side.

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