Shortening a long antenna with a capacitance
A monopole antenna (for example) at exactly one quarter wavelength will project an impedance of about 37 ohms resistive and about 20 ohms reactive (inductive). At longer lengths it will project more resistance and more inductive reactance and close to 0.47 wavelengths it will be highly resistive and have neglible reactance as per the diagram below: -

 

So, if you want to tune a long antenna with capacitance or a short antenna with inductance that's fine but be aware of how the resitance (a projection of the resistance of free space) will change significantly and how the cycle repeats itself at 3/4 of a wavelength.


  An inductor is added to counteract this, basically lengthening the
  antenna electrically.


It's somewhat incorrect to think this way - all the inductor does is counter the inherent increase in capacitive reactance (by series tuning) thus leaving just the resistive component (and this will be very much smaller than the resistive component at a more appropriate length). 

The impact of this is that the signal received is much smaller so, it's not really lengthening the antenna at all; it's tuning out an impedance that could block the now much smaller signal being received.

If you take that into account then certainly tuning a long antenna is fine but somewhat pointless in many applications where resorting to an antenna of about the right length will yield much more favourable results.