Is the convention of dropping the leading 1 when storing the significand a given in all binary floating point representations or not necessarily?
As @BugKiller says, if it is IEEE format, it doesn't matter how many bits (32, 64, 43, etc) uses your representation, you drop the leading 1. And I think is the same thing with subnormal numbers taking a leading 0. Other floating point representations not specified within IEEE takes the same idea, because this dropped 1 comes from binary representation as any non-zero number will have a leading one, you drop it and you gain 1 bit to expand your representation.
The convention of dropping the leading 1 is not universal among practical floating point implementations. Namely, the very common x87 extended precision format does not follow this convention.