This is a hard question to give a definitive answer to. So I'm going to point out some pieces that may help you examine it. Ultimately, there are some pieces that remain unanswered in your setting that may impact the answer. I will try to address these.
Please note that this question invites biased answers, because it is a question of human nature, and philosophers have argued about these topics since the dawn of recorded history, and still haven't come to anything like an agreement. I apologize in advance for any non-objective input in this answer.
First off, a thing that wasn't clear in your setting...
In short, if there are still rich and poor, then with an unlimited life, the rich will get richer...and the poor may remain poor their entire lives. If you are barely eking out an existence on the edges of society...it may be worth risking your life rather than spending eternity barely surviving.
Existence of Tyrants
These have existed since...pretty much always. You get someone who says 'obey me with a risk of death, or face immediate death.' Well, he has conscripts to fight now. Then others, if they want to stop him, must build armies as well. After all, you don't get a war if only one side is ready to fight. They generally call that a massacre, not a war.
Eventually, if you live forever, you are going to run out of crap to do. You only have one risk that is a real thing. Death. Anything else...well, you can recover from it in time. So the only real thrill is something with the risk of death.
This is the piece that, as I warned, shows my bias about human nature. If you disagree with me, then for the purposes of your story, ignore this block. I don't believe that people are intrinsically good. There will always be those who want more than they have...and there will always be those that don't care who they have to hurt to get it. That is, after all, a fair definition of a Psychopath. Also, I believe that there will always be ideological differences that people are willing to fight for. And, if you remember, old people tend to be even more set in their beliefs than someone younger, and can be rather belligerent in defending them. Add in the human-nature 'Us Versus Them' mentality (want to demonstrate it? Look at sports team fans and the fans of their rival team), add in a few thousand years to let it all steep...and you have a recipe for some very deep seated hatred.
So, in conclusion...I don't think that agelessness would mean the end of war.