[BigOz]

LiFePO4 batteries are considered not to decompose like other Lithium cell types, e.g. Liithium-ion or Lithiumi-ion polymer (LiPo) which can be very impressive when they go.
It will get very hot if abused by overcharging and in extreme situations may emit white smoke but I've not heard of one deflagrating as the other types do. It is certainly possible they get hot enough that other items in the locality will reach their auto ignition temperature if it is close and not a material suited to high temperatures.

Your battery is likely a 4sXp (four cells in series and some number in parallel to give the cold crank rating depending on the output rating of the cells) setup which means the maximum charge voltage is 14.4 or 3.6V per cell and without an in built protection circuit in the battery (which some have) if your reg rec outputs more than 14.4V (it should not) you will overcharge your cells.
At 15V or 3.75V per cell I'd bet that would already be damaging the cells in so far as it would be limiting the life of the cells.

If nervous I'd consider a small voltmeter added to the instruments.