Even if DA3 screws up somewhere along the line, I imagine Bioware still has too much inertia for that to be their death knell. If it does fail for some reason though, Bioware will likely be seeing cutbacks from it's owner EA.
When EA bought Bioware, they were preparing to make the company a leading brand name for EA to publish a number of titles under, from RTS to mobile gaming, Bioware was originally intended to be one of the crown jewels in EA's lineup. It's somewhat telling that EA has rescinded its name changes of other studios that they were tacking the Bioware name onto, and have basically halted plans to make Bioware a centerpiece of their collection. Likely, EA is wary at this point and is waiting to see how things change before they commit to making Bioware a flagship studio ala EA sports or shunting its production solely into Bioware core titles (which will likely end up with EA forcing Bioware to make another Mass Effect game). If it gets bad enough EA may attempt to rename the studio or lay off staff, forcing Bioware to work on a limited production budget.
People forget that critical acclaim and financial success take a backseat to meeting financial predictions and sales expectations set by the publisher. ToR was a decent MMO and sold pretty well, but its massive budget caused it's sales and retention rates to fall well short of company predictions. For anyone that followed the sales for ME3, after the ending controversy started the sales of ME3 dropped fast and EA admitted that the sales of the game post launch were short of their expectations. ME3 did still sell well though, so I doubt EA is looking for it's shotgun just yet, but two games in a row being unable to meet demands set by the publisher means they are probably going to adjust their expectations downward in the future, meaning that Bioware gets less of the EA money pie. They certainly aren't going to let Bioware develop another MMO anytime soon.
Could DA3 be the end of Bioware? I doubt it, but it could be the point where Bioware is no longer seen as the juggernaut of western RPGs that it once was. Of course, if DA3 sells phenomenally then it's also possible that EA will once again go ahead with its plans to make Bioware the center of many of its future production products. They could end up like Westwood, once being pretty much the premier RTS maker, eventually shut down after dropping sales over time, or they could end up like the Sims developers, shunted into a niche perhaps, but EA is still willing to pump time and money into new titles from them. In some hypothetical best case scenario they could even turn it all around and sell massive amounts of copies, where EA will restart its plans to make Bioware an entire division unto itself. It's really all speculation at this point. While I don't think its a lynchpin, DA3 will likely set the tone for Bioware going forward in the future.