linux-image-2.6.24-12-virtual contains e1000e, but not e1000. If VMware server is configured to present an e1000 NIC to the guest, the e1000e driver does not detect it. This can be reproduced by adding the following line to the .vmx vmware guest config file:
ethernet0.virtualDev = "e1000"
However, if linux-image-2.6.24-12-server is run in the guest, the e1000 module successfully identifies the virtual NIC presented by VMware, and loads. The numeric PCI ID of the e1000 virtual NIC presented by VMware is 8086:100f - perhaps this is not probed for by e1000e?
lspci shows "Ethernet controller: Intel Corporation 82545EM Gigabit Ethernet Controller (Copper) (rev 01)"
FWIW, the vmxnet module bundled with the -virtual kernel image works successfully when the guest .vmx file has ethernet0.virtualDev = "vmxnet" in it. This requires that VMware tools has already been installed in the guest however, whereas most modern distros/OSes should have the Intel e1000 driver included.
To answer my own question, after scanning the source of the e1000e driver, it appears it does not look for PCI ID 8086:100f - therefore will not load for the 82545EM NIC emulated by VMware.
The e1000 driver will need to be added.