Recently, spin selection rules have been invoked to explain the discrepancy between measured and calculated adsorption probabilities of molecular oxygen reacting with Al(111). In this work, we inspect the impact of nonadiabatic spin transitions on the dynamics of this system from first principles. For this purpose, the motion on two distinct potential-energy surfaces associated to different spin configurations and possible transitions between them are inspected by means of the fewest-switches algorithm. Within this framework, we especially focus on the influence of such spin transitions on observables accessible to molecular-beam experiments. On this basis, we suggest experimental setups that can validate the occurrence of such transitions and discuss their feasibility.