Yes, you can have two exactly (or almost) versions of the same plugin so long as the plugin names are different. Of course, you can enable only one or you will get conflicts.
Depending on what the things specific to you theme are, you can also pass paramters, even optional ones, that modify the behavior. So, for instance, you could pass a function as an optional parameter. Then the plugin could test if the function was passed and if so, call it.