I certainly would expect so. One of the many possible examples: if a frugivore strongly prefers the fruit of species A, then, seeds of all other plant species that are consumed in an opportunistic manner by the same frugivore (say, species B, C and D) will be likely deposited beneath mother plants of species A.
Nice question Andrew, it is fun to think about it! If we are talking only about avian seed dispersers, then I would agree with José, but in the case of carnivores the answer would not be so clear because of theit longer transit times and the secondary role of fruits in their diet. So, if we focus only on avian seed dispersers, I would propose that to the extent that they are gape limited in their fruit choices, we should find a higher density and diversity of dispersed seeds under small fruited species. If this were true, small fruited species could have a relevant role in maintaing the diversity of fleshy fruited plants in the community.
Yes, in many direct and indirect ways. The fate of seeds is tightly linked to a frugivore's feeding preferences. For instance, some animals visit different kinds of habitats, depending on where their favorite fruits grow. Thus, seeds of different species may be carried to unfavorable or favorable sites following different probabilities, depending on where the frugivore collects the fruits, eats them, and defecates. See some papers:
1.Levine, J. M. & Murrell, D. J. The Community-Level Consequences of Seed Dispersal Patterns. Annu. Rev. Ecol. Evol. Syst.34, 549–574 (2003).
2.Levin, S. A., Muller-Landau, H. C., Nathan, R. & Chave, J. The ecology and evolution of seed dispersal: a theoretical perspective. Annu. Rev. Ecol. Syst.34, 575–604 (2003).
3.Schupp, E. W., Jordano, P. & Gómez, J. M. Seed dispersal effectiveness revisited: a conceptual review. New Phytol.188, 333–353 (2010).
4. Muylaert, R. L., Matos, D. M. da S. & Mello, M. A. R. Interindividual variations in fruit preferences of the yellow-shouldered bat Sturnira lilium (Chiroptera: Phyllostomidae) in a cafeteria experiment. Mammalia78, 93–101 (2014).
5. Andrade, T. Y., Thies, W., Rogeri, P. K., Kalko, E. K. V & Mello, M. A. R. Hierarchical fruit selection by Neotropical leaf-nosed bats (Chiroptera: Phyllostomidae). J. Mammal.94, 1094–1101 (2013).