Will the armour piece where I put Protection affect its effects?

No.

While the mechanics of enchanted armor are different in 1.8 and 1.9, the protection enchantments reduce damage equally, no matter on which armor piece they are placed. There is a formula on the wiki to calculate the extra protection from enchantments (in 1.9):

The EPFs of all applicable enchantments are added together and capped at 20. The damage is reduced as damage = damage * ( 1 - cappedEPF / 25 ), giving a maximum reduction of 80% at EPF 20.

Only the total (capped) EPF (Enchantment Protection Factor) is used for the calculation, and EPF calculation is the same no matter what armor piece you are looking at. This is true for both 1.8 and 1.9.

I also ran some tests in the 1.9 pre-release right now. I created a 3x4x3 obsidian box with water at the bottom (to prevent burning), and a single block window at one side as well as the top open. The window was used to trigger a set of command blocks to teleport me into the center of the box and summon a Fireball with Explosion power 3 above myself, heading downwards:

/tp @a 59 57 1
/summon Fireball 59 70 1 {direction:[0.0,-1.0,0.0],ExplosionPower:3}

I put on a diamond helmet, boots, and chestplate, one of which was enchanted with Protection IV. The fireball consistently did 4 Hearts of damage, regardless of which armor item was enchanted. Without any enchantments, the damage was 5 Hearts.

I conducted an experiment to test your question(In 1.8.9) and the answer was NO. First I tested each piece of leather armor without any effects: Boots: Chestplate: Helmet: Leggings:

Each test with normal leather armor ended with the same amount of damage taken. I had jumped from a height of 11 blocks and tested each armor piece one at a time with leather so the damage would be more significant and easier to read. You could probably draw the conclusion from this, but I decided to test just to make sure. I gave myself Protection 2 leather armor and repeated the test. I used a command like this:

/give @p leather_helmet 1 0 {display: {Name: "hat"},ench: [{id: 0,lvl: 2}]}

Although the damage was decreased by half a heart the damage taken with each one on stayed the same. As a last and final test I gave myself Protection 4 armor and jumped from a height of 15 blocks to make sure that my data didn't change. ...As I had expected the data didn't change and the damage taken was equal even on different pieces of armor. I received a damage of five hearts on each of the last jumps with the different individual armor pieces.

This test should prove that enchantments don't change the defense value depending on the armor piece within one set.