What happens if the Central Bank does not absorb a BOP deficit/surplus?
If OA is a part of FA. The second equation follows from the first:
$CA + KA = FA \wedge OA \neq 0 \Rightarrow FA - OA = CA +KA -OA \neq CA +KA$.

Response to your EDIT:

$CA + KA \neq \frac{FA}{OA}$ follows from the first equation as well:

$CA + KA = FA \wedge OA \neq 1 \Rightarrow  \frac{FA}{OA}= \frac{CA+KA}{OA} \neq CA +KA$ in general. (I've checked your LateX expression it really says: "(FA \backslash OA)"). I don't understand why you would think that BOP has anything to do with division. For example Feenstra and Taylor say in their textbook:

$OSB=-Reserve FA=CA+KA+Nonreserve FA$, where OSB is your OA and their version of the BOP identity is $CA + KA + FA = 0$, with your FA as their -FA.