There are some authors proposing that. For instance:

Gur, Y. & Breitbart, H., 2006. Mammalian sperm translate nuclear-encoded proteins by mitochondrial-type ribosomes. Genes Dev, 20(4), pp.411-6.

Zhao, C. et al., 2009. Role of translation by mitochondrial-type ribosomes during sperm capacitation: an analysis based on a proteomic approach. Proteomics, 9(5), pp.1385-99.

However, many RNA could be just remains from spermatogenesis, although some types could play an important role post-fertilization. Not only mRNA, but also other kind of RNAs. For instance:

Krawetz, S.A. et al., 2011. A survey of small RNAs in human sperm. Human reproduction (Oxford, England), 26(12), pp.3401-3412.

Sendler, E. et al., 2013. Stability, delivery and functions of human sperm RNAs at fertilization. Nucleic acids research, 41(7), pp.4104-4117.

Thanks for the references. My perception of the subject is as follows:

                                    The Art of the Matter

Microtubules (MTs) form the life line of all diploid cells of various shapes and sizes including metastatic cancer cells. In short, these are involved in intracellular transport of vesicles/materials with the help of motor proteins as well as promote cellular motility. Microtubles are formed of alpha and beta tubulins. The MTs are of two kinds-stable and dynamic. In the diploid cells both types co-exist and could be subserving different functions within the cells. MTs also constitute the motility cytoskeletal apparatus of cilia, flagella and sperm. MTs are responsible for the forward motility function of haploid sperm. In the diploid cells, MTs can be formed wherever needed for example spindle formation during cell division or motility of metastatsizing cancer cells, or even neuronal migration during brain development. However, in motility appendages like cilia and flagella, these exist in a fixed position and arrangement(9 + 2). This arrangement permits them to initiate sliding motion and maintain motility. Historically, Calcium dependent depolymerisation/polymerisation of the tubulins has been reported to form the basis of an escalator/treadmill like motion by the dynamic fraction of MTs. Acetylation of alpha tubulin at K40 positions is deemed to stabilise the tubules through the activity of a HAT/TAT (histone acetyl transferase). Deaectylation of these acetyl groups destabilises the MTs through the activity of the enzyme HDAC6 (histone deacetylase)-a MAP (microtubule associated protein). The latter enzyme has been implicated in forward sperm motility. It is however a moot point whether calcium plays a role in association of this MAP with tubulin fibers, subsequent deacetylation/depolymerisation, and sliding motion of tubulin subunits. It is another moot point whether this would occur in tandem with PKA cascade and activation of dynein ATPase or subsequent to the latter activity in order to facilitate the type of spot-hypermotility which sustains the journey of the sperm by dissolving the cumulus to the plasma membrane of the oocyte. The authors have reported that HDAC6 inhibitors increased acetylation and restricted motility. In all likelihood, MAP association with MTs was affected thereby restricting the deacetylation and sliding motion. Could this have led to a compensatory increase in putative translation of hdac6 transcripts by mitochondrial-type ribosomes in sperm? It is not yet understood why only one out of several million sperm succeed in fertilising an ovum. Perhaps it has to do with the mechanisms of motility management. One argument that has been suggested is that X chromosome bearing female sperm are heavier and therefore would move less rapidly than Y chromosome bearing lighter male sperm. The two major functions that the sperm must accomplish are forward motility to reach the ovum and fertilisation (to deliver the genetic material, possibly at a defined acceptor site (not a random one) at the plasma membrane, considering the post-fertilisation embryogenesis is strictly spatially (and temporally) programmed. When one sperm accesses this site all others are rejected). The success of fertilisation depends thus upon an optimum function of the motility cytoskeleton. In view of this, the sperm translation of motility related hadc6 transcripts could assume importance.