Yes and no. 4% HP and 4% DEF on accessories both increase effective HP by 4% when no other source of stat in question is present. So if you have 100% increase in HP from weapon grid, 4% HP from acc becomes 2% effective HP increase. Same with DEF, if you have 100% increase in DEF, 4% from acc becomes 2% increase in effective HP.
Now then, do you have 100% DEF increase ?
But wait, there's more. DEF increase not only effective HP, but healing power too. Let's make such an example.
10k base HP, some kind of 2k heal, mob hits for 4k.
With 100% HP increase: Kamihime health pool equals 20k, she gets hit for 4k and healed for 2k. That leaves us with 18k HP.
With 100% DEF increase: Kamihime health pool equals 10k, she gets hit for 2k (4k * 1/(1+1) = 2k) and healed for 2k. That leaves us with 10k (full) HP.
So DEF is better in almost all cases than HP.
It's most probably not and tbh I am not sure where people got this idea of "double is rolled first". From my short tests I suppose that values above 100% are scaled to 100%. So for example if you have 200% double attack chance and 200% triple attack chance, it will result in effective 50% chance for double attack and 50% chance for triple attack. Does that mean that double above 100% chance for combo reduces chance for triple ? Yes, but it doesn't mean 2% increase in double will reduce triple by 2%.
Now, if anybody is interested why scaling. It's probably because devs were lazy and it was easier to make guaranteed combo attack buffs. You can just slap 200% double attack increase and 50% triple attack to get the guaranteed combo attack with probability of 80% DA and 20% TA (not exactly, but lets say it's close enough).