Are Desmond Doss's ultra-pacifistic views actually biblical?
In short, no.
But, first, let me say that this is an interesting real-life tale that needed to be told and the movie is a good war flick only marred by laying on the heroic element too thick in the last act as well as the lack of depth in the peripheral characters, which makes them uninteresting. The latter is in contrast to the outstanding "Platoon" (1986) which featured several well-defined characters.
The movie's about an individual -- Desmond Doss -- who believed in ABSOLUTE pacifism, which is a peaceable attitude that refuses to ever turn to violence, even in response to evil or for the purpose of national defense. He thinks this is supported by the Bible and, specifically, the New Testament, but it isn't.
The Christian Scriptures support LIMITED pacifism, which is a peaceable attitude that only resorts to violence when justified. Christ's instructions to "turn the cheek" related to responding to a backhanded slap to the face, which was an insult in that culture. In other words, we could all save ourselves a lot of trouble in life if we learn to ignore the antagonism of various morons who would like to divert our focus and ruin our day. The Old Testament teaches this as well: "A fool shows his annoyance at once, but a prudent man overlooks an insult" (Proverbs 12:16). So Christ was talking about giving an antagonist a break for the sake of peace in situations of personal offense; he wasn't referring to cases of severe criminal acts or defense of one's nation.
For proof, Jesus' ministry team had a treasury box and some of his workers carried swords for protection from thieves/murderers in their travels. You see, Christ & his disciples weren't absolute pacifists.
On two occasions, the Messiah got a whip out and chased all the fools out of the Temple - throwing over tables, swinging the whip and yelling. He was a Holy Terror, pure & simple, and this caused the legalistic religious leaders to fear him and plot murder (John 2:13-17 & Mark 11:15-18). Harmless pacifists don't inspire fear like this.
Moreover, Romans 13 clearly states that the righteous laws of human governments are ordained of God for the purpose of punishing criminals, domestic & foreign, who threaten the lives of citizens. This includes the right to execute when appropriate. The passage puts it like this: “they are God’s servants, agents of wrath to bring punishment on the wrongdoer.”
The majority of sane Christians realize this, but there are a few extremists, like Doss in the movie, who refuse to be balanced with the Scriptures on this matter and insist that violent conflict is never appropriate. Wrong. Sometimes it's necessary, like after the Japanese attacked Pearl Harbor, unprovoked, murdering over 2300 innocents and wounding 1100, or when a piece of sheet thug threatens your kin, physical or spiritual. The recent justified shooting of an evil assailant intent on mass murder at a Texas church assembly is a prime example: https://www.foxnews.com/us/texas-church-shooting-man-take-out-gunman-west-freeway-church