Can "ты ещё нас всех переживёшь" have a positive connotation?

It has only positive connotation, HOWEVER the speech style of this very phrase is very informal, like pat on the back, which in the context of granddaughter speaking to grandmother might be considered rude, disrespectful. Ofcourse usually most grandmothers will let it slide, but theoretically there is a chance to be offended. So in would be fine for a slightly younger close friend to say it, but not for a much younger person.

To quote a well-known Russian book: "Я всех вас переживу. Вы не знаете Паниковского. Паниковский вас всех продаст, купит и снова продаст, но уже дороже." Here "Я всех вас переживу." (I will outlive all of you.) has the meaning of "I will dance on your grave" or "I will come to your funeral in a red dress."

The phrase implies a bitter conflict between the interlocutors and that they may rejoice at the death of the other. In the context of the question: the granddaughter essentially implies that the grandma has ill feelings towards the rest of the family and may rejoice when all of them are dead.

The correct English translation of "ты ещё нас всех переживёшь" is "you're still going to outlive us all", which is obviously intended to mean "you still have much potential, much life force, so much that it will suffice for you to live longer than all of us". However, ещё is a polysemantic word, apart from its adverbial meanings "still, yet, already, additionally" one of its meanings is "so far" (пока что, meaning 4) and another (meaning 11) is to show reproach, irony, like in "Ты ещё скажи, что собаки летать умеют!" Also, it can express concern:

Надо позвонить, а то ещё решат, что мы погибли.
Let me call in, lest they think we're dead.

А то еще на вопросы отвечать придется…
Don't want to answer any questions…

The last three meanings and especially the last one can interfere with the correct understanding of ещё in your phrase, instead of wishing long life the phrase can be understood as the speaker's concern that grandma can outlive them. If the grandma is paranoid enough, she can understand the phrase as "so far, you can outlive us all[, but we'll take measures needed to prevent that]" or as "[don't you try to] outlive us all".

To resolve the ambiguity and make the phrase really inspiring and cheerful, the word ещё can be just omitted, or moved to another clause or sentence, for example:

Ты ещё много всего успеешь, да ты и нас всех переживёшь, у тебя ещё много хорошего впереди!