Can EPOLLHUP trigger an event for a descriptor, disabled by EPOLLONESHOT?

Can EPOLLHUP trigger an event for a descriptor, disabled by EPOLLONESHOT?

I have a few threads, waiting on the same epoll_fd with epoll_wait(). The
descriptors within epoll set are setup in this way:
struct epoll_event event;
event.events = EPOLLIN | EPOLLONESHOT;
event.data.fd = fd;
The purpose of EPOLLONESHOT is to guarantee, that each descriptor is
handled only in one thread at the same time. If one thread has received
EPOLLIN event with specific fd, can the EPOLLHUP or EPOLLERR trigger event
in another thread with the same fd?
I suggest they can't - since the descriptor is disabled due to
EPOLLONESHOT. But if they can - can I use EPOLLRDHUP instead? Will it be
triggered at least once when the descriptor becomes
invalid/closed/disconnected by any means?