Let's say you have a Wireguard configuration, wg0 which runs off ens0. If your wg0 connection dies, for whatever reason (let's say the remote server goes down), your computer falls back to ens0.
What does "not having a connection to be maintained" change about this?
I guess, too much magic automation on top of this is not the best thing for opsec, including having some daemon that can disable your wireguard interface or reconfigure the network if it doesn't like something. You want your network configuration to be static and predictable, regardless of some temporary failures. Basic wireguard kernel primitives will give you that.
So... You'd have to do work to properly blackhole traffic when wg0 goes down. However long it takes to reconnect, you still will automatically fall back down to ens0 while it's down unless you do something to stop that.
Packets are always delivered to wg interface as long as it is marked as 'UP' (or 'enabled', if 'UP' sounds to you like having anything to do with some kind of "connection") when your routing table directs them there.
When they hit the wg interface when the other endpoint is unreachable for whatever reason, they are either dropped, or queued, or get ICMP unreachable response generated for them, depending on situation. This is done internally by wireguard.
If you wanted to not go through wg0 (whether it can reach the other wireguard peer or not) you'd have to remove the routes first.