Yeah, they definitely would have either closed down or seriously downsized without EA. TBH, i would prefer if they had done a kickstarter or something (i liked their pre-EA games better), but i'd agree that it's better this way than closed down.
Then again, the entire Mass Effect series is technically post-acquisition, so there's an argument to be made there. (Well, they had to have been almost done the first one before EA took over, so that might explain why it's my favourite in the series, but the point stands)
On topic: EA did save them. If they weren't bought by EA back then, the studio would have probably closed down. If that was happening today, they wouldn't need EA, they could have gone *indie* and use gofundme/kickstarter to fund their games. Bioware has some really hardcore fans, some even before the ME series!
I freaking loved Bioware before EA. I still love Bioware now. EA may have saved them, but they definitely dampened the creative genius of the studio. While I can appreciate the studio being saved, I am not a fan of the corporate soul crushing.