So this sort of a setup is called Dual-WAN, and yes, it allows it all to work. Basically, my router has two connections to the internet- a cable modem on one port, which connects to Spectrum, and a cell modem on another port, which has my sim card on it. Both provide internet access simultaneously. My router is then configured to reach the internet via what it decides is the ‘best’ internet. In my case, because my cell connection is metered, I have it configured so that it prefers the spectrum connection, and only falls back to the cell connection if the spectrum connection is losing traffic, and only for as long as that connection is losing traffic. Note that a dedicated cell modem is not necessarily required- some routers have sim card slots themselves, for exactly this reason, and tend to make this sort of configuration very simple to do. I’m personally using a small computer running OPNSense, which is again, probably overkill for the average homelabber, but you don’t need something that complicated.

As a result, my server always has access to the internet, and should you configure your firewalls appropriately, the internet will then always have access to your server. There’s some details here and there about IP address caching, dns resolution, and the like which have various solutions from DDNS to an external proxy/loadbalancer/etc, but those are more implementation details.