That is what remains to be seen. The EU has never been called to defend its members before. It, and NATO, included the Baltics because they petitioned to join and, in the days after the fall of the USSR, it probably seemed like the right thing to do. The "end of history," ex-Soviet states wanting to be like the West and all that.
In practice I'm skeptical about the rest of the EU/NATO's willingness to truly fight and bleed for them. There are still those who see them as nothing more than post-Soviet states in Russia's backyard. Hell, there are still western Europeans who are blissfully unaware that the Baltic states have their own, non-Slavic languages; I've met them.
Since any Russian offensive would be swift, and since Putin would not attack unless he knew he could win quickly, odds are the EU/NATO would have no chance to join the defense and would have to evict Russian occupiers with a counterattack. I can't see them having the will to do that. Germans don't have the will to fight. Most of the rest of western Europe would have a rather anti-war public that could argue they're a safe distance. I could see Poland having the public support to resist...but not alone, and odds are they'd be alone. And America under Trump cannot be trusted to oppose Russia militarily, no matter the circumstances.
So I really have no trust in EU/NATO willingness to contest the Baltics.