No, not necessarily.
At least, no more than, say, a cow's milk allergy means that one shouldn't be breastfed on human breastmilk.
There's a matter of cross-reactivity and similarity in endocarp proteins at play-- I have no idea just how closely related kola and almond are... but it seems highly unlikely to me that there is much cross-reactivity.
That also assumes that the derivative is even protein-based to start with.
KWIM?
Is the "kola nut" actually the ENDOCARP? Or the drupe? This is the difference between, say, eating a peach versus an almond.