no you dont. Ive done it and you keep the parts - you just have to click them when you select your car in your garage (I think its settings or tunning or something) and they will be improving your specs again after you race modify it.
it says right on the race mod option in the auto shop that you will lose any mods you made to the car. whether that doesnt apply to some parts i dont know.
You basically waste credits on redundant upgrades like weight reductions and transmission, etc.. Best bet is to buy a car and then RM first, then go into the other upgrades.