Does FXLoader support period end and period average rates in R12?

Yes.

For period average, FXLoader can calculate the average and store it in a separate rate type.

For period end, you could just use the same rate type as you load daily rates into, if this contains the rate needed for the last day of the period. Otherwise, you can just schedule a separate run of the daily rates program to load a different rate type on the last day of each period.