yes. if you feed the speakers 20w, then it should output 20w.
additional:
it can be safely fed with a steady signal (sine wave) of up to 110w, but since sound is has irregular bumps and dips, those speakers can take up to 220w for brief periods. keep your amp up to 110w rms only. this is just a practical view.
more additional:
consider your amp as well. rms value (root mean square) is a mathematical calculation of the nominal or steady power output. this is the rating that you want and not pmpo (peak music power output) which is deceptive. on a ten scale vu leds, pmpo would be all leds lighting up momentarily at the bang of a drum while rms is a more constant 3 or 4 leds for the rest of the song.
my $5 amplified pc speaker is advertised as 200w pmpo yet it contains a 2w chip.