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This is typically correct, however is fully dependant of the module you use.
i.e. whmcs has a cpanel module that allows you to sign clients up and automatically provision their account on the cpanel server.
This works for many services however does rely on a module for WHMCS
Yes this is possible and there are in fact a few solutions for this. Typically you will have a server with VPS management software and have that software's corresponding module in WHMCS. You would then be able to create VPS templates and allow WHMCS to set these template up for your clients when they sign up.
There are a few modules referenced on the documentation (http://wiki.whmcs.com/Server_Modules):
HyperVM
FluidVM
SolusVM
Cloudmin
VPS.Net
To add to this list I would also like to mention another product that I know has a WHMCS module:
Virtualizor
Whilst I could recommend two of the above products, I would suggest that you review them all and then ask people of their experience with some of them (at this point I'd be more than happy to suggest the two I personally like). This way you will be able to make an informed decision based on your exact needs without being bias from the word go.