Distortion that is visible on an oscilloscope means your are generating energy at multiples of the fundamental frequency.
If that matters depends on how much energy you are radiating to some extent.
If you are applying a couple of volts to a couple of meters of wire as an antenna then the radiated ERP will be very low because your antenna is very small compared to the wavelength.
The chance of someone within a few hundred meters of you noticing that your toy medium wave transmitter is putting out weak carriers on shortwave frequencies is low.
If you are planning to use a large antenna and significant power then yes you should have a clean output spectrum. Emissions on 1.6MHz, 2.4, 3.2,4.0MHz etc could go a long way.
Of course if you are doing that you should also worry about the stability of your oscillator, crystal control is strongly preferred for transmitters so the frequency does not drift.