No, the Israeli army doesn’t save Jewish lives. Quite the contrary, as we explained at length elsewhere.
But even if they did, that does not logically mean you should enlist!
Rabbi Avigdor Miller employs pure logic:
Q:
How could you say that a person should avoid military service in Israel when there are millions of Jews living there who have to be protected?
A:
… So I’m asking this gentleman here, the questioner, what’s he doing here? Why is he a slacker?! There are millions of Jews who have to be protected; let him go and join up. The answer is, you have your reasons. You think, maybe, that right now you want to study here, and become a physician and eventually, you’ll go there and you’ll help them out in that way. So you have an idea to help the people there in a different way, not by putting on a uniform right now. That’s your idea of helping them. It sounds reasonable.
So we also have ideas of helping the people in Eretz Yisroel. And one idea is to send a lot of money to the yeshivos, to poor talmidei chachamim. The money goes into the economy. Any money you send is going to be spent there; it’s spent in the butcher shops and in the grocery shops. It’s spent on products, and you’re therefore supporting the people who work in the factories. Whatever money you send to talmidei chachomim living there goes straight into the economy. It’s very important. Believe me, if you asked the people at the head of the state, “Would you excuse about twenty, or fifty, or a hundred or a thousand people from the army to go to the United States and raise big sums for your economy?” They’d gladly agree because money is the blood of a nation. You can’t make war without money…