The Eurozone (Germany mostly) is getting closer and closer to Russia. I don't think Latvia will gain any advantage from this.
Take a look at what happened to Cyprus. They (the EU) would never do that to Italy, no matter how crisis-striken would ever be. Meaning: Say tomorrow Russia invades Latvia, the EU will do a couple statements and that's about it.
How an attack on a EU member state will be reacted to will set precedent. The EU cannot afford not to react to such an attack with full military force no matter which member state is attacked.
Apart from that the majority of states in the NATO are also EU member states, meaning that the EU has effectively control over the NATO. Also something that might be worth considering in such a scenario.
On the other hand, the baltics are primarily of interest to Russia as a buffer against invasion from the west, so it is at a time of antagonism between Germany and Russia that Latvia would most need to fear Russian invasion.
Latvia can always invoke Article 5 of the NATO treaty, anyway.
Take a look at what happened to Cyprus. They (the EU) would never do that to Italy, no matter how crisis-striken would ever be. Meaning: Say tomorrow Russia invades Latvia, the EU will do a couple statements and that's about it.