Phospholipid membrane fluidity if phospholipid had one type of fatty acid
Cell membrane doesn't have just phospholipid inside.

Components who influence fluidity in cell membrane are:

1) Fatty acids length 
2) The grade of unsaturation of these fatty acids 
3) Presence of cholesterol


So, if composed of just fatty acids, excluding every other component (carbohydrates, channels proteins and, mainly, cholesterol), the answer would be yes, its fluidity will change drastically.