VMware frequently does not use VT, because their technology often provides better performance than is possible with VT. E.g., VMware Workstation allows you to enable VT use, but the default on my machine is to not use it. In fact, usually VT needs to be enabled in the BIOS, because there are attacks on VT (and similar technologies) such as the BluePill attack that are pretty scary.
See for example this link, which is about VMware Server not needing VT:
The links you provided are about trying to run VMware ESX server, VMware's bare-metal hypervisor (runs directly on the host machine, without a host OS), inside of VMware Workstation or Player. This is a very unusual configuration, primarily used for testing ESX. If you think about it for a moment, it will make sense that running VMware's most powerful product within one of their other products requires some special support.
As far as 32-bit and 64-bit, I think I've run 64-bit guests within my 32-bit host OS without enabling VT, but I'm not sure. VirtualPC is not a fair comparison, because VMware basically invented x86 virtualization more than a decade ago.
Honestly, downloading and running Player will be pretty quick. If you have an Ubuntu ISO, you can simply mount that and run it as a LiveCD within player. Actually doing Ubuntu installation doesn't take that long. Windows Server installation will be slower, but I would bet that it will work.
Once you've got things set up, you might look into using VMware Server, which is also free, and more powerful than VMware Player.