First a quick note: The mini USB cable on that will not fit into the pi. The pi uses a micro USB and they are not the same shape. However, you could still use it, keep reading.
Am i right in saying that although 3 amps are available, the pi will only draw what it needs?
Yes, that is how electricity works. However, beware that stuff connected to the Pi can cause a draw exceeding the limits of the polyfuse on the microUSB supply jack, so unless you want to experiment with seeing how long that takes to reset (or what it can handle...), avoid that. I believe the limit is 2 A on all models but the 3, which is 2.5 A.
Also beware if you backpower via normal USB or one of the 5V pins this polyfuse does not provide any protection. Presuming this 2-3 A limit is there for good reason, in that case you want to make absolutely sure no more than that will be used.
If I were doing this I'd chop a microUSB cable and wire it to the supply so you do not have to backpower. This also ensures the power goes through the onboard regulator first (which it certainly won't do via a 5V pin).
It may also be possible to get a mini->micro USB adapter.