For a gaming/general use desktop would a discrete NIC be notably better than onboard?

Currently on 1Gb fiber with onboard Killer E2500(sans bloatware.) Would one of the lower-end network cards using Broadcom or Intel chipsets improve network performance or quality and CPU utilization?

Yes.

Appreciably? Very likely no. Depending on how your system is set up and what compromise needs to be made to install a discrete NIC, it could make things worse.

I've had onboard some Realtek NICs shit the bed under prolonged heavy load, in my case VMs on some network storage: iSCSI or maybe an NFS share. Under less stressful conditions I'm sure onboard is fine. Unless you see stuff acting wonky I'd hold off. You could try benching with Iperf and stress testing what you have now and see if it's a problem. If your onboard NIC can't handle it grab a cheap Intel NIC off eBay like the HP NC360T or Dell X3959.

Eh, my onboard NIC does TCP offloading... not sure what else you might want. I would rather go without the NIC and perhaps have better airflow without an additional card.

For playing games, probably not. Most local installed games don't push either NICs or bandwidths. What helps most games is low ping times.

Now downloading games and other large files might benefit from a better NIC but only if your current one is sucking in some way.