As much as it might seem implausible that VII and X are connected to so many of you, it has been officially stated that they do in fact take place in the same universe. However, I do not believe that the Shera in DoC is one such connection. It is my belief that it is just a cameo. Remember in FFI, you had to dig up an airship that ran off of some unknown technology? Well, I think that they just put a similar thing in DoC nothing more.
Hell, if you wanted to use that as a connection, you might as well say that all of them are connected. After all, every single FF game either mentions Cid in conjunction with airships, or actually has him as a character that flies airships. Anyways, to sum up, VII and X are connected, it's official. Spirans are pre-Gaians. Nomura and Kitase said it, so get over it if you don't like it.