What prevents mRNAs that are localized to a specific part of the cell from being translated before they reach their destination?
The answer to your general question is 'it depends':


A lot of RNA localisation to the ER and mitochondria happens co-translationally (based on the protein targeting sequences), so these mRNA actually depend on translation to be localised. However, RNA localisation to mitochondria can also happen due to targeting sequences in the mRNA 3'UTR - in these cases translational repression would be possible, but it's unlikely and I don't think anyone ever checked it in this particular case. (see i.e. this review)
the translation of many mRNAs that are actively transported along the cytoskeleton is inhibited during transport, either by specific RNA binding proteins or larger RNP (ribo-nucleo-protein) complexes (see another review). 


There are also bound to be some specific mRNA that have very specific regulation mechanisms and others that are exceptions.