I doubt she would have lasted the entire series as well. Their dysfunctional relationship was brilliant and I loved how her and uncle June were like a tag team nemesis to Tony. They helped keep him in check so to speak and the series lost that with her death and Junior's role in the series changed once the show lost that element. I loved Junior but once his role in the series changed/was minimized he should have been killed off(or simply died during the cancer scare).
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I imagine they would've killed Tony's mother off at some point anyway, but it's an interesting question. There's a real lack of focus in series three and four, and I'm sure things would've been different with Nancy Marchand around.
Lack of focus in three and four? Those seasons are pure gold compared to the final two seasons. While season six had a few really good episodes, it was a cluster fuck. Tony basically had a skeleton crew, the NJ crew did not seem to be as powerful as we were led to believe in the beginning, and it felt like they were just making it up as they went along. The all out war that occurred in season six should have happened in 3-4 between Tony-Johnny Sack- Carmine during that Espanade(however you spell it) ordeal.. Would have been stellar as most of the great characters were still alive at that point.
I really enjoyed season three, but it lacked that killer storyline that seasons one and two had. Season four I thought was a mess. Felt like they'd run out of ideas and were just kind of stumbling along. The last episode was great, but all the aggro between NJ and NY before that felt really forced and didn't go anywhere. I remember at the time Chase was looking to finish after four series, and HBO talked him into doing another. It might well have just been him trying to get a pay rise, but it felt like he'd just gone "well, I was planning to end it here, but now I've got to pull a new series out of nowhere to fill the gap", and as such they didn't really seem to know what they were doing.
Season five was better. They definitely seemed tapped out of ideas at that point, but doing a bit of a reboot with a bunch of new characters helped somewhat. It was a bit slow in places, but again it ended strong. Season six I've pretty much forgotten the first half of - easily the most hit and miss of all of them. Frank Vincent was brilliant, and the penultimate episode would be a strong contender for my favourite one ever, but yeah... overall not great. I think they knew the story they wanted to tell, it just wasn't anywhere near big enough to fill all the episodes they had, so they came up with a lot of filler.
Just got free HBO for the summer also so can even watch it legally 
