If it develops it's own fanbase and brings DA into the online era, it would indeed make more money...And further any agenda they may have to develop a fantasy-based MMO.
From a design standpoint: It has no effect on SP. The "wrong decision" is subjective to opinion. You think it is, but that is not a fact. If more people buy the game, Bioware wins.
Arguing that one's personal wants for a franchise is "untrue" to the series is inaccurate. Bioware (owned by EA or not) devs. are the only people that know the true direction of the series and it's up to them where it goes from here.
Also, EA bought Bioware. It wasn't involuntary. If, somehow, EA were holding Bioware creative ideas hostage, then it's their own (Bioware's)fault for selling out. EA is a big corporate machine. It's obvious now and it was obvious back then.
No, the MP clearly uses resources from the SP campaign or the other way around. They had to be working together and that means time, money and people had to be assigned to coordinate it, at the minimum.
You think MP is treated like a completely different game but the fact is that the engine, the animations, the sound effects, the voice overs, the level design and more had to be done for SP first and then adapted to MP. Adapting takes away resources.
The MP feels even less complete than the SP, so please don't tell me it was the correct decision to include it in this form. They might be able to improve it a lot through DLCs (as they did with ME3 MP) but right now it's a mess. And the SP suffered for it.