No. A very weak signal can be boosted by a mixer, but speaker level signal will only produce distortion if fed to an amplifier. Amplifiers are designed to produce the max power from a relatively small signal. If you want a cheap amp it's easier to buy a used one on Ebay/gumtree, or even get one free on Freegle/Freecycle. If you want to use just one speaker , a stereo amp that's faulty on one channel will be very cheap/free, and it will still work for what you want.
Used car amps are cheap but you need a power supply that can deliver 1 amp at 14 volts to power your "15 watt" speaker.
there's a really good Adastra active speaker called Speak- Eazy, Loud Mouth & some other names, it has an on-board cassette deck (of v. poor quality) or a CD player, and puts out 20 watts. When new it comes with 3 Wireless microphones and has a 6mm mono jack input for a wired mic. as well as phono inputs for a music player of some sort. They are about £120 new but can be got much cheaper used. Great value for money.