I highly doubt that J is alive...she was indeed a very sinister character for pokemon...Not showing an ounce of respect or consideration for people or pokemon...when the price was right, she'd stop at nothing to get what she wanted, and wouldn't allow for anyone to get in her way...And just for that, I think it would be more appropiate for a character like herself to be terminated in death...
Some of you people, like poizonsting, are wanting an article, or something from the writers to prove that she's dead...Well, unless you write to the creators of the show themselves, you'll only have to go with what was given to us, and that's basically what we've been doing.
There was far too much symbolism that would represent the termination of J and her team. For one, while she was attempting to catch the lake trio, she was directly attacked with their Psychic energy...damage represented in her damaged visor. Who knows how much pain her body sustaind from that? After that, when she got back on her ship with her crew, the ship was struck with the Pixies' Future Sight attack.
While the ship was going down into the lake's torrent whirpool thing, that would've been the perfect opportunity to call out her Salamence or one of her pokemon for an escape because the ship was going down, and the crew couldn't do anything to get it working.
As the ship was going down in the depths of the water, J's visor was sinking down along with the ship. Now, something like that may represent that J may have had a very small chance to make an escape from the water, but smaller than her chances before. But that could also mean that as the water crashed into the ship, it could've washed away her visor as she sank to the bottom of the lake with the ship.
And last but not least, there was the explosion. Now, this kind of explosion isn't the same as the kind of explosion that Giovanni escaped...This one is an explosion where J was closer to the source of the explosion, which would mean that her body and the rest of her crew would feel the impact of the explosion very quickly. For the explosion, the waters crashing in, and J's delayed action to make a move combined, along with all of that symbolism just makes me think that J is no longer alive. But that's just how I see it.