The AKG C 480 series is typical of most "modular" microphone series (i.e. product lines with one or more standard amplifiers plus a larger number of interchangeable capsules), in that the microphone amplifiers are designed to be as sonically neutral as possible. They usually have some bandpass filtering but they have to work with a variety of different capsules, so they don't use audio response-shaping circuitry.
That's a real advantage as far as sonic consistency from sample to sample is concerned. Whenever there's audio response-shaping circuitry built into a microphone amplifier (e.g. the Neumann U 87 or most Sennheiser MKH microphones), there will always be particular components whose precise characteristics determine the sound of that individual microphone, and thus some variation in sound quality from sample to sample of the amplifier. In a sonically neutral circuit on the other hand, the quality control issues are simpler, and individual amplifiers don't generally sound different from one another.
The overall gain (amplification factor) of the amplifiers of one series from a good manufacturer might fall within a tolerance limit of perhaps 1 dB overall. A half-decibel shift in balance between the channels of a stereo recording can definitely be audible; still, that difference can usually be fixed up with a tweak to some setting somewhere "downstream." Or if you know which of your capsules is more sensitive than the other, you can use it on the amplifier that has the lower gain, and even things out that way. So in practice, as far as microphone amplifiers (bodies) are concerned, AKG isn't wrong; it shouldn't generally be necessary to select matched amplifiers in pairs for a series like this from a good manufacturer.
Capsules are another kettle of fish because their function is so much more complex; they are acoustical and electronic components at the same time, with one foot in each universe so to speak. Their tolerance limits might be within a total of 2 dB or 2-1/2 dB overall, and that would be from the better manufacturers--the cheaper ones (or the cheaper lines from manufacturers that have some lines of microphones that are deliberately made more or less carefully than others) will have a wider tolerance field.
If you're going to make critical recordings with a single pair of main microphones--and especially if you will be using coincident or closely-spaced microphone setups--a matched pair of capsules can offer audible advantages. The quality of stereo imaging depends on having two microphones with the same sensitivity and frequency response as each other, both on and off axis. The variations occur at both ends of the frequency range (but especially the high frequencies) and in the change in response as you measure farther and farther off-axis, but also in overall sensitivity (normally measured on axis at 1 kHz).
Ironically it's microphone amplifiers that always get a serial number put onto them; most manufacturers hide or (during production but after testing) remove their capsules' serial numbers if serial numbering is used for them at all. Consecutive serial numbers are thus pretty much just a beauty thing--nice for the collector in all of us, but not very meaningful when it comes to predicting how the microphones will behave as a pair.
One well-known manufacturer, in line with this way of thinking, offers selected, matched pairs of capsules on request at extra cost. They don't offer selected, matched pairs of amplifiers, however, since the differences among amplifiers of the same series are a straightforward issue of gain, not sound quality. Another well-known manufacturer has recently begun offering "stereo sets" in some of which the capsules are selected as matched pairs and then placed on bodies (amplifiers) that have consecutive serial numbers. That's a nicely thought-out approach which should please both the knowledgeable technician and the collector.
--best regards