pg_upgrade question

Hello all,

We're running a 13.x installation and looking to upgrade to 14.1.  This
is all on Linux servers.   We have a main instance running with a number
of hot standby replicas configured.   In the past, we have done a
dump/restore on a slow evening and then rsynced all the bits around so
that the main server and all replicas were identical at the start.   The
database has gotten larger now (~1TB) so that is a less desirable option.

So I am thinking to do a pg_upgrade --link on each of the main and the
hot standby replicas, and then restarting all the processes.   I'm sure
this will work fine on the main server, but I have not seen any mention
of this working in the expected way on the hot standby replicas.   Can
someone confirm that the steps I described here will work in the way I
am optimistically expecting it will?

I should mention that we are running on ZFS, and will take a snapshot
prior to the upgrade, so that if something goes sideways with our use of
--link  we can revert back instantly. 

Thank you,

Alan