What is the lifespan of a Gungan, how old was Jar Jar in the Episode I–III trilogy, and when does the VII–IX trilogy take place in reference to the I–III trilogy?
Most sites quote the lifespan of a Gungan at ~65 years. The source for this figure seems to be the Ultimate Alien Anthology, which goes into slightly more detail about Gungan age and lifespan:
Age in Years: Child 1–12; young adult 13–15; adult 16–35; middle age 36–54; old 55–64; venerable 65+.
According to his Wookieepedia entry, Jar-Jar was born in 52 BBY. It references Star Wars: Episode I Insider's Guide, a game which discussed details of the expanded universe, but I haven't found a copy of the original entry in the game.
In March 2014, Disney and Lucasfilm announced a timeline for the VII–IX trilogy:
It has also been confirmed that Star Wars: Episode VII is set about 30 years after the events of Star Wars: Episode VI Return of the Jedi, and will star a trio of new young leads along with some very familiar faces.
Since Return of the Jedi is set in 4 ABY, this puts Episode VII around 34 ABY. This means Jar-Jar would have to be at around 86 at the start of the new trilogy. The ages above don't put a Gungan living to 86 outside the realms of possibility, but I would think it's fairly unlikely.
1) Their life expectancy is 65 years (Wookieepedia)
2) Approximately 40 years passed between episode 1 and 6. The 7 is supposed to take place at least 20 to 40 years after the episode 6. Jar Jar would need to be a maximum of 5 years old in the episode 1 to be still alive by then.
3) . Lucas said that only C-3PO and R2-D2 were the characters that would make it through the nine Star Wars films (Wikipédia)
So the answer is probably "no".