Could GPU hangs be causing network drops on these ThinkPads?

I'd try to separate the network symptom from the system hang before settling on a cause. Ping working only tells you that ICMP gets through. It doesn't tell you whether a TCP connection is leaving the interface or whether the affected process can run normally.

When a machine is in that state, use Test-NetConnection against a known host and port if you can open PowerShell. A packet capture at the same time may show whether connection attempts are actually being sent. It would also help to note whether outbound connections fail while existing connections still work, and whether new processes or UAC prompts can open.

The dock and wake pattern is worth testing on its own. Try a small set of machines undocked, then docked with external displays, and compare what happens after sleep and resume. Include both graphics configurations if possible.

Also check BIOS, dock firmware and graphics drivers, not just the Wi-Fi driver. The NVIDIA machines freezing harder doesn't rule out a shared trigger, since the Intel-only machines are affected too.

Since resume is a common trigger, I'd investigate Wi-Fi power management too. A network adapter that doesn't resume cleanly can produce odd connection problems. Testing a policy that prevents the adapter from sleeping, or temporarily disabling sleep on a test machine, might help narrow it down. Either way, that would be a workaround to test, not proof that the GPU hang caused the network failure.

One troubleshooting lead is TCP checksum offloading. Disabling it in the network adapter's advanced driver settings has been suggested for connection failures on an Intel i225-LM wired adapter. Your machines use AX211 Wi-Fi, so that isn't a direct match, but it may be worth checking whether the setting exists and testing it on one affected laptop.

Can you reproduce the hang in Safe Mode with Networking? That could help narrow down whether something loaded in a normal Windows session is involved. I'd also try disconnecting and reconnecting the dock when it happens, if the machine is still responsive. That has restored a connection in a similar docked setup, though it doesn't explain the underlying fault.