FWIW, I'm not using a proxy and I'm able to "curl -I https://vmwaredepot.dell.com/index.xml" from the VCSA and get a 200 OK

Same here.

log in VCSA via Putty

You have to Run the following command stop the update manager service :

service-control –stop vmware-updatemgr

Run the following command to reset the Database of VMware Update Manager:

/usr/lib/vmware-updatemgr/bin/updatemgr-utility.py reset-db

Run the following command to delete contents of the VMware Update Manager ( this will delete the contents of the VMware Update Manager)

rm -rf /storage/updatemgr/patch-store/*

You have done with fix , now start the pdate Manager Service and log out and log in .

Start the VMware Update Manager Service:
service-control –start vmware-updatemgr

All the best
Ajith.P