R2D6 is the one that gives an EPT.
Will this combo allow me to discard the droid to not take a damage, and keep my EPT?
R2D6 and integrated astromech
Yes. The official FAQ has said so. Same applies to someone using Boba Fett crew to discard the droid - you still keep the EPT. In general, upgrade cards that grant further upgrade slots at the beginning of the game don't ever cause you to lose those upgrade slots when discarded.