Well, some Links have been known to time travel quite often. Just look at MM, OoT or OoA. So this might be possible.
I don't think that the TP Link is a decendant of the Hero of Time Link. Do you know the split timeline theory? At the end of OoT, Link travels back in time to warn everybody about Ganondorf. However, the future Ganondorf is still locked away in the Sacred Realm in the adult timeline, while Link traveled back. So there isn't a Hero of Time anymore in the adult timeline, but there is Ganondorf. That means that all the Links in the adult timeline games (TP and WW) aren't decendants of the Hero of Time Link. Therefore they aren't Heroes of Time, but they are new types of Heroes, like the Hero of Winds. So the Link in TP isn't the Hero of Time.
There is also a story, which I beleive was thought up by someone on GameFAQs. Before the final battle against Ganondorf, Hyrule is already flooding. All the residents flee away, except for Link. Nobody knows about Link, except Zelda off course, so everybody thinks that nobody ever arived to save them. Link knows that if he will battle Ganondorf, he won't be able to flee in time and he will drown. But he also knows that if Ganondorf won't be fought, he will be able to get away from the flooding and will be able to continue taking over the world. Link also knows that if Ganondorf won't be beaten, he will be able to resurface and take over the world, as Ganondorf is somewhat immortal. The only way to defeat Ganondorf is by locking him away at the bottem of the now forming ocean. And the only way to lock Ganondorf away is to defeat him in a fight.
And there even if Link did die, there is a Zelda after that. WW happens about 100 years after TP and Phantom Hourglass comes after that.
So to sommon up, the Link in WW, the Link in TP and the Link in OoT are not related in any way. I think Link will die in the end when Hyrule floods over. WW and PH come after TP and PH will be released after TP.