If a reaction absorbs energy does that mean it has a net gain of energy?
We use several quantities called 'Theormodynamic Potentials' to measure the 'energy' or, more accurately, the state of the sustem. Examples would be Gibbs free energy, Helmholtz potential, Internal energy etc. In a general chemical reaction performed in lab (at constant pressure and constant temperature), Gibbs free energy provides an intuitive way of determining the direction of a spontaneous reaction. A reaction always proceed towards minimizing Gibbs Free Energy.
You are probably asking about enthalpy of a reaction being negative or positive, which 'in special cases' corresponds to the heat exchanged during the reaction. In those special cases, exothermic reaction does imply a positive enthalpy change i.e. products have higher 'potential' (referring to enthalpy here) relative to reactants.
Notice how I carefully use 'potential' instead of 'energy' since the latter is quiet vague and may refer to any of the several potentials defined in thermodynamics.
Once you give enough energy to reactants to cross the activation energy barrier it would react to Form the compounds, if the net energy is released, then the products will have lower potential energy or else (as in your case) the potential energy of products will be more than that of reactants