I'm installing Ubuntu on my SSD and don't want to waste space on a swap partition because I have 16GB of ram, nor do I use hibernation. But as a precaution, would there be any drawbacks if I created a Swap on my 3TB storage drive that is shared with Windows 7?
You would not notice any difference unless you ran out of RAM. At that point, there would be a monumental slowdown no matter if you used SSD or HDD. (Unless you have one of those fancy PCI-SSD things that are new from Intel.) However, if you plan on hibernating your computer, then there would be a slightly faster performance increase on the SSD.
When editing /etc/fstab, remember to mount and partition correctly. Backup your windows partition when resizing with
Note: Hibernation is disabled by default, as it is not compatible with many computers.
The amount of storage that you allow for the swap area to be created over is taken from the storage you allot your Ubuntu partition to reside in. This Ubuntu partition will be protected as long as you do not erase or destroy it through another booting from a live CD or through similar mechanism. So there will be no drawbacks when you share your HDD with other OS alongside Ubuntu.