As far as the speaker is concerned, there is no risk of any damage to the speaker in an acoustic amplifier from using an overdrive (OD) pedal at the input (i.e. pre-amp section) of the amplifier. The speaker responds to the signal/power provided to it by the power amp section of the amplifier circuit; over-driving the pre-amp with a pedal is not going to turn -- say -- a 100 Watt amplifier into a 200 Watt amplifier, nor is it going to effect impedance matching, etc. The power-amp and speaker combination are simply going to *amplify* the signal provided.
So....no worries to the amplifier's speaker.
As far the circuitry of the input section of a solid-state acoustic amplifier, my limited knowledge makes it harder for me to offer a all-encompassing opinion.
Classical transistors are pretty tough, but most modern solid-state amplifiers employ a pre-amp circuit which is composed of Integrated Circuit (IC) chips, and I am far less fluent in ICs. Speaking of OD pedals ("stomp boxes") in general, however, they more primarily effect the character of the signal, and to a lesser extent increase (boost) the amplitude of the signal. The input of the amplifier really does not care a whiff if the incoming signal is already clipped by a pedal; it might care if the incoming signal was so heavily over-boosted that the signal exceeded voltage tolerances for the amplifier pre-amp, but this would be very extreme for any pedal. In general, the input of a solid-state amplifier will regard the increase in voltage provided by an OD pedal the same as if one were using a compressor, clean boost, EQ pedal, etc., to raise the signal for a solo. It will not care *what* the signal sounds like, it will just amplify it.
I say go for it if it sounds good to you.
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