I've only used a few examples from many
ARISTEIDES (HE) ‘They appeal to those who wrong them and make them friendly to themselves; they are eager to do good to their enemies; they are mild and conciliatory.’"18
IRENAEUS (180 A.D.) "For the Christians have changed their swords and their lances into instruments of peace, and they know not how to fight."24
TARAKHOS (304 A.D.) "Tarakhos of Cilicia, on trial because he had left the army, told the governor he had been a soldier, ‘but because I was a Christian, I have now chosen to be a civilian.’" He was martyred in 304 A.D.59
http://www.heraldmag.org/olb/Contents/doctrine/ecvowams.htm
Fair enough, that's what some of the church leaders were saying (although some of Tertullian's early writings, for example, said they were just like any other Roman citizens, up to and including "fighting" - he later changed his stance). In practice, though ...
We know that there were Xians serving in the legions, from stories such as that of the "Thundering" legion, composed of, or mainly of Xians, under Marcus Aurelius in the Marcomanni Wars, and the "Forty Martyrs of Sebaste", said to have been martyred under Licinius - these and other like stories would have had no plausiblility if it had been known that Xians refused service in the legions;
From barracks churches in Meggido and Doura-Europa, the former containing an inscription stating that its mosaic floor was the gift of a centurion, the latter being in a fortress settlement with virtually no civilian population;
From purges in the army such as that under Diocletian - how do you purge Xians from the army if there are no Xians in the army?
The evidence from purges and martyrdoms would also suggest that it wasn't the having to fight that was the cause of those soldiers' problems with the army, but the fact that they were forced to either sacrifice to the state gods or leave the legions (losing their status and pensions). This is in line with what we now of most Roman "persecutions" of Xians; that the problem wasn't their belief in Xianity, but their refusal to honour the state gods.
So yes, in theory, the early Xians were, or were supposed to be, pacifist, but in practice they didn't all live up to that ideal. That's why I say the claim is doubtful or, if you prefer, debatable.