No, you can't just add the speaker in by itself. You would need to use the crossovers and speakers from a car that uses 3 speakers in each front door so that the correct frequencies go to the correct speakers.
As for your speaker issue, you may have some broken wires or broken insulation of your door wiring loom where it passes through the rubber boot between your door hinges. I had this problem myself recently.
Not a specially difficult job to check, just time consuming. I was able to do it easily though as I already had the door card and door skin off. You can see my photos of the wiring in my posts in the 'what did you do to your Mk5 today ' thread a few ago.
To remove the door card you need a plastic trim removal toll and T20 & T30 torx keys. For the door skin it's just the two torx keys.