Characterizing the mechanical properties of tissues is key for the understanding of fundamental biological processes such as morphogenesis or tumor progression. In particular, the intercellular adhesion forces, mediated by transmembrane proteins like cadherins, are expected to control the topology and viscoelastic behavior of tissues under mechanical stress. In order to understand the influence of adhesion in tissues, we use biomimetic emulsions in which droplets mimic cells and adhere to each other through specific bonds. Here, we tune both the binding energy of the adhesive inter-droplets contacts as well as the fraction of contacts that are adhesive, thereby defining a so-called adhesiveness. Our experimental results show that adhesion prevents the emergence of local order in emulsions even at high packing fractions by preventing energetically costly droplet rearrangements. By studying the deformation of droplets within packings with different average adhesiveness values, we reveal the existence of a threshold value of adhesiveness above which all droplets in a packing are deformed as adhesive ones irrespective of their local adhesive properties. We show that this critical adhesiveness coincides with the threshold for percolation of adhesive structures throughout the tissue. From a biological point of view, this indicates that only a fraction of adhesive cells would be sufficient to tune the global mechanical properties of a tissue, which would be critical during processes such as morphogenesis.