Not necessarily...in an idealistic world - the idea of 'engagement' is to accept/acknowledge a person for a long term relationship called marriage. 'How' one expresses it is completely an individual choice and the strength of their relationship. There have been couples in history who celebrate this happy day by slipping a mere rubberband or a thread onto the ring finger, and have survived! After all, a diamond is merely a piece of rock...!
However, if its a social requirement where the couple is expected to follow some or all of the 'traditional'/ 'religious' or 'to prove their social status' etc...then its mostly non-negotiable.
The final motive is to settle down for life with the one you love...how you celebrate each milestone is based on your understanding towards each other/ personal strength...and most importantly - your pocket!! Afterall, which woman would not like to have a shining diamond to display?