before answering your question i want to explain what is granjer causality test.  it test that whether lags of one (independent) variable helps to predict (granjer causes) other (dependent) variable. So if theoretically their is a relation between two variables whether one is index or what ever it is, we can check granjer causality. secondly as granjer causality is based on VAR model which alternatively places each variable as dependent then if there is theoratical justification (endogenity of variables) then we can perform granjer causality. third, if variable is non stationary of higher order then 1st or/and secon difference can be included. 

endogenous and exogenous is a theoratical concept. so if one variable is exogenious out of two then obviously VAR cannot be run. its alternatuve can be that we run a model with exogenious as independent variable and run the wald test for joint testing of lags of exogenious variable which is kind of granjer causality test for single equation.

Unless there is something unusual about your index variable that you have not mentioned then the fact that it is an index should have bearing on: whether it is endogenous or exogenous; whether causality tests are appropriate; whether differencing is appropriate.

Thanks Vince Daly 

and now without the embarrassingly crucial typing error:

Unless there is something unusual about your index variable that you have not mentioned then the fact that it is an index should have NO bearing on: whether it is endogenous or exogenous; whether causality tests are appropriate; whether differencing is appropriate.

Vince Daily (after the typing error...) is correct.