That really, really depends on the amp (and the acoustic guitar).
Like the comparison I drew between my MT15 / 50w Stealth.. The MT can't get much quieter than an acoustic guitar before the volume is just off whereas my Stealth can get quieter than my electric strings ringing acoustically.
I've played a Gibson acoustic that made all the other guitars in the room resonate. Then on the other end of the spectrum with the Yamaha Silent or that paddle-shaped travel guitar that is barely audible.
@Boudoir Guitar +1 My Epiphone ES 335 sounds like a quiet acoustic. It has been my new 'round the house guitar but the body size makes it a tad awkward.
IMO, OP you have two seperate problems you aim to solve here - playing when people are sleeping, and playing while competing with other noise.
Unless you're trying to tick both of the boxes at once.. If I'm wanting to play guitar in the living room during TV time, nobody will sleep. My kids' rooms' are pretty close to our living room so I go into my room with my quieter gear. That may not be the case for you?