If you mean accessing them from within your LAN while your internet is down then no it won’t work.

What you should be doing is either split horizon DNS (LAN resolves local IPs, public resolves public IPs) or use different DNS hostnames internally, for example media.local.yourdomain.com

You then set up a reverse proxy in your LAN and point everything to that, use a let’s encrypt wildcard cert using the DNS challenge method so you can get *.yourdomain.com protected with a single cert. Since you use cloudflare you can use the cloudflare API plugin with certbot, it’ll automate everything for the DNS challenge and no need to keep opening ports or configuring http/https challenges every couple of months.