From the FFX-2 Ultimania Guide (Translation from gamefaq.com (
http://www.gamefaqs.com/console/ps2/game/562386.html)):
***Interview with FFX-2 creators from the Final Fantasy X-2 Ultimania***
(Page 723)
**"So, what of this child, Shinra......"**
--"Among these latest stories, 'connected' is one of the key words becoming
applicable, isn't it?"
[Daisuke] Watanabe
"I personally like the word 'connected,' but there's one aspect where that
applies well."
Nojima
"During the game's progression, various vague things will be tied together to
reveal it."
--"For example, the name 'Shinra' suggests a connection with VII? There's
[what's said] in the 'Graduation Mission' scenario [ -- 'graduation'
referring to Shinra being soon to leave the Gullwings -- ], and the 'I am not
alone in my thinking' line from the 'Rin's Detective Work' scenario seems to
have some particular significance."
Nojima
"Actually, it does. After quitting the Gullwings, Shinra received enormous
financial support from Rin, and began trying to use Vegnagun to siphon Mako
Energy from the Farplane. But, he is unable to complete the system for
utilizing this energy in his generation, and in the future, when traveling to
distant planets becomes possible, the Shin-Ra Company is founded on another
world, or something like that....... That would happen about 1000 years after
this story, I think."
--"So VII's story is after that?"
Nojima
"Well, you could say the feelings I have are like that. When I think about the
characters, those are the kinds of feelings I already have. Shinra is a good
child, but his descendants are going to end up becoming like the president [of
Shin-Ra] (laughs)."
Watanabe
"With you said about VII, after seeing your episodes with Shinra, one of the
people on the [development] staff said that the first shot of the Bevelle
Underground 'gives the impression of somewhere else.'"
[Motomu] Toriyama
"Certainly; it looks like the opening shot of Midgar in VII."
So in other words there is kind-of-sort-of-maybe a connection between the two games that could either be considered canon or Nojima's random musings.