No.

If the source is not balanced, there is no advantage to using an XLR connector on the other end, in fact it may be worse. A single ended signal has two paths, 1) signal and 2) ground. A balanced signal has three, 1) signal, 2) signal in opposite polarity, and 3) ground. The idea of balanced is that path one and two can be used to reject noise that entered the cable.
Lets say for example (very simplified) that airborne noise causes a +3db rise at 3KHz. This would affect both the 1) signal and 2) opposite signal. At the end of the cable, the device (preamp, amp, whatever) will put together the 1) signal and then invert the 2) opposite signal to be the correct polarity. Ideally the two signals should now be identical, but since the noise caused a +3db rise at 3KHz, and since the polarity of 2) the opposite signal was inverted, that signal now has a -3db drop at 3KHz. Put them together and they cancel out, no more noise. The magic of this process is called common mode rejection.
This is why there is also no advantage to running a Balanced cable to a component that is not truly "balanced".
Hope that helps!