Brehs, can a experienced Systems Administrator (with a Network+ cert) crossover into a Network Administrator job OR is her gonna have get some Cisco certs?
I guess similar questions to this would be:
Can a experienced Systems Administrator (with a Network+ cert and/or Security+ cert) crossover into a Security Administrator job?
Can a experienced Systems Administrator (with a Network+ cert and/or Cloud+ cert) crossover into a Cloud Administrator job OR is her gonna have get some AWS/Microsoft Azure/Google Cloud certs?
It really depends on the company. Some care a lot about certs, some care more about experience.

Personally I'm a Systems Engineer who does a decent amount of stuff with routers/switches and I don't have any Cisco certs at all (been putting it off for ages). But I've been where I work for a while and moved up from Desktop Support so they trust me. If it was somebody off the street they'd probably care more about certs.
Brehs, can a experienced Systems Administrator (with a Network+ cert) crossover into a Network Administrator job OR is her gonna have get some Cisco certs?