Yeah I think so, even the lenght of the leader has an effect on this I think.
About carp hooks, there are specific hooks depending if you use classic or pop-up/other rigs.
For example the Zenith Mugga hooks seem to be made for pop-up rigs (read the description):
But even with the right kind of hook, false bites/failed strikes will happen anyway.
How many times I got my boilies stolen by carps IRL... depends of the fishes! Some fishes are super cautious, they will take the bait between the lips without taking the hook in the mouth, they begin to pull and bye bye boilie ^^.
The same for live/dead baitfishes, particularly if you use simple hooks (not triple).