That's possible, yes.
There are methods of turning your current windows environment into a virtual machine, so if you have lots of available HDD space you could try something like this:

• clean up what you do not need
• install linux aside windows as a dual-boot OS
• now you can use linux or windows, whichever you choose
• clone your windows into a VM
• run the VM inside linux to make sure everything works
• delete the original windows installation and free up space
• profit...

Now that's an interesting idea indeed! I am afraid that is not very easy to achieve, however that is not impossible. Hibernation is performed by stopping all running processes and writing the current total RAM content into a file on HDD, and on restore it is read back and processes are unfrozen.

In theory it is possible to have 2 different files on your HDD, one containing the current windows RAM image and one containing the current linux RAM image.
The going-to-hibernation-phase is easy, I'd say some quick patching of the hibernation code is enough to make sure each OS can go down gracefully.
The wakeup phase is more difficult, You'd need to write an utility that can select which OS to wake up to and chainload correctly the image unfreezing.
Doable, but could prove a challenge. (I could propably fix up something like that for the linux part fairly easily but I have no idea how to implement the windows side of it....)