I would think so, but not seeing your speakers I couldn't say for sure. If your outdoor speakers are all 8 ohm and you parallel them to the unit (making 4 ohm) I would think it would do the job. I would certainly try it. The Lepai seems to be rated down to 4 ohm speaker impedance. Looks to be Bluetooth only, no wifi. There are certainly other amps you could look at, though I would recommend avoiding PYLE and some of the other really low end brands. They are pretty much horrible in many ways.
Parts Express also sells a Bluetooth receiver module that could drive a larger amp if needed. You already have a volume control. Or go the route georged suggested and get "The Who" volume levels
Parts Express also sells a Bluetooth receiver module that could drive a larger amp if needed. You already have a volume control. Or go the route georged suggested and get "The Who" volume levels