Stick to the same color pallet througout entire home?

Sounds lovely to me! If you like it - it works. Decor choices are very personal. Remember Sara Richardson on HGTV years ago when she bought a house and every episode was a different room? On some of her homes she kept the color pallet similar throughout the entire home or at least the entire level. One house she did, she used a different color in each room, but was tied together by style of furnishings she used. Your home is an expression of you and your family. If you love something you will find a way to work it into your design. I kept a similar color pallet through my house as it is tiny and semi-open concept - except my office. I went for a different look altogether. When I go to sell the house, that room will be repainted as it is too taste specific and would put people off. So use those colors but do not be afraid to have a different accent color in each room if you so choose.

Sounds very pretty

Do you have an open floor plan or no? Do you want to decorate your house in a cohesive colors?

I think the corals and turquoise accents would go perfect with grey walls and white trim. in my home I used grey semi-gloss and white oil based paint. It takes longer to dry but looks so much more professional and is much more durable. With the grey and white you can always change your accent colors without having to change the wall color. Sounds very pretty.

Sounds lovely like a beach theme. Pillows, throws, rugs, pictures all if these will add those colors and add pop of color to your gray and white.