By means of Monte Carlo simulations we study jamming and percolation processes upon the random sequential adsorption of dimers on binary alloys with different degrees of structural order. The substrates are equimolar mixtures that we simulate using an Ising model with conserved order parameter. After an annealing at temperature T we quench the alloys to freeze the state of order of the surface at this temperature. The deposition is then performed neglecting thermal effects like surface desorption or diffusion. In this way, the annealing temperature is a continuous parameter that characterizes the adsorbing surfaces, shaping the deposition process. As the alloys undergo an order-disorder phase transition at the Onsager critical temperature (Tc), the jamming and percolating properties of the set of deposited dimers are subjected to nontrivial changes, which we summarize in a density-temperature phase diagram. We find that for T<T*=1.22Tc the occurrence of jamming prevents the onset of percolating clusters, while percolation is possible for T>T*. Particular attention is focused close to T*, where the interplay between jamming and percolation restricts fluctuations, forcing exponents seemingly different from the standard percolation universality class. By analogy with a thermal transition, we study the onset of percolation using the temperature T as a control parameter. We propose thermal scaling Ansätze to analyze the behavior of the percolation threshold and its thermally induced fluctuations. Also, the fractal dimension of the percolating cluster is determined. Based on these measurements and the excellent data collapse, we conclude that the universality class of standard percolation is preserved for all temperatures.