Can I connect an amplifier to a Crystal Radio?
The crystal radio gets all of its miniscule power directly from the energy in the radio signal that it picks up. It is tiny. As a result it can only power a high impedance (high resistance to AC signal) crystal earpiece. The input impedance of these is typically 20 kΩ. (This surprised me as I always considered them much higher.)

Your guitar amplifier, on the other hand, is designed to amplify a signal from a guitar pickup. This will be much-much stronger than the radio signal and so the amplifier may not be sensitive enough to play it loud.

It won't damage anything to try and should be quite instructive.



Figure 1. Crystal earpiece innards. Source: The Trouble With Ceramic Earpieces made by Eagle or Altai and Others.

Thanks to @robert bristow-johnson for correcting me on earpiece theory. I found an interesting article, linked above, which goes into some detail on the internal construction.