Li Pings Lifepo4? A little light in my opinion. More better for a 300 watt bike. What is the wattage of the amped controller? I have the 35 amp WE controller and my Ping 1.0 can put out 20 amps safely. Most ebikes pull around 12 amps when running full speed on the flat. I figure some of my ride exceeds the 20 amps but not all of it. For you, when you pull 20 amps or so starting, or hill climbing, you will be farther above the safe zone for discharge rate.
Will it cut out? Some folks had problems with 10 amp batteries (10ah) and fewer with 15's. If you live in real flat territory you should be ok, if you live in hills, no. Either way, under 20 ah duct tape batteries get stressed more than 20 ah or larger. So the stressed battery can't possibly deliver the same number of discharge cycles. Depending on how you use the bike, maybe who cares? If you will ride 10 or more discharges a week, it could cost ya. If you will ride 3 or 4 charges a week, you will never get to the point where number of discharges matters.