@MattHooper It’s perfectly safe as long as you match levels, which is what I mean by your bold text above.
If your recording device has, say, a maximum input voltage of 2 volts RMS, then make sure the power amp isn’t putting out more than 2V RMS at its speaker output.
A simple, fail-safe* way is to set the power amp to a gain of 1. That is, play a sine wave through the DAC, measure its voltage output from the DAC outputs, then connect it to the power amp, and adjust volume until the power amp has the same voltage output at its speaker output.
* I suppose, technically, if the DAC connected to the power amp has so much output voltage that it could damage your recording device by itself, then this isn’t as fail-safe as I thought. But seriously, in that case the DAC could technically damage the power amp too…this would be very unusual.
@BDWoody the level matching I describe achieves the same thing more simply.