What to check before attempting a read-scale replica log backup?
Log backups are important.  If they are scheduled to be run every 15 minutes, for example, that means they need to run every 15 minutes in order to meet you RPO.  Although it's nice to have the secondary running log backups, it is not nice if the log backups fail, and then you have a catastrophe at the primary site and you don't have recent log backups--you will not meet your RTO.

I would recommend that you run the log backups on the primary if possible, and have them copied to another location at the primary site, and also to the secondary's site.  This way you have the log backups available at the primary site, and this covers you in case you have a problem with the primary server, but the site survives.  If the entire site goes down, you have the latest log backups possible, given the network instability, at the secondary site.

I would inform management that due to the network instability, you cannot guarantee the RPO at the secondary site, and have them approve whatever plan you implement.