It is possible to create your own "simple" MOBI dictionary, and these are reported to work on the Kindle. For example, see
change primary dictionary to English2Chinese.
What isn't typically possible is to use a commercial MOBI dictionary on the Kindle. Even without the DRM, these dictionaries usually invoke MOBI features that are not supported on the Kindle.
However, there are now a few primary translation dictionaries for sale in the Kindle store. At Amazon, browse the following list (currently 13 results):
Kindle Store › Kindle Books › Reference › Dictionaries & Thesauruses › Kindle Default Dictionaries