Yes, Christian new wave does exist. Following is a list of Christian artists who have done new wave or dabbled in the genre:
77's -- Most of their "All Fall Down" album is very new wave, though some of their blues and classic rock roots shine at times. One of my all time favorite albums, that still sounds fresh today. It's a masterpiece. They also did a tiny bit of new wave on their first album "Ping pong Over The Abyss", including the track "Renaissance Man" (which would later be covered by The Ocean Blue).
Vector -- Their first two albums "Mannequin Virtue" and "Please Stand By" are in the new wave style, some of the best Christian new wave ever produced.
Weber and the Buzz Tones -- They only recorded 4 songs, on a self titled EP. I'd like to see this on Cd someday, though you can probably find a digital download of it. Very synth oriented new wave rock. They were my #1 favorite Christian band when I was 12 years old (I'm almost 40 now).
Quickflight -- I still have their "Decent Beat" album on cassette. Very good, though it's lost some of it's freshness.
Daniel Amos -- They did some new wave in the 80's, some of it sounding like a cross between the Talking Heads and The Eagles, or new wave meets The Beatles. Their Vox Humana album is perhaps their most new wave effort. One of my favorite songs from them is "Mall (All Over The World)".
Terry Scott Taylor -- The soloist from Daniel Amos. His "Knowledge & Innocence" album is fairly new wave for the most part. The one track "Light Princess" reminds me a bit of Psychedelic Furs.
Steve Taylor -- He dabbled in new wave in his earlier days, including the song "Am I In Sync" (later covered by Circle Of Dust).
Steve Scott -- Yet another new wave dabbler, a perfect example being the tune "Love In The Western World".
November Commandment -- They put out a fantastic E.P in the 90's called "Exile Station". Very Depeche Mode in style, with an industrial flavor. It doesn't score high points for originality, but very high points for quality tunes and production. They also recorded one track for a Blonde Vinyle compilation album, though not as good.
Jamboree -- I have one 5 song album by them called "Melt Down". I'm not sure how new wave it qualifies, but it has some of that new wave flavor to it. There is one track on the album that I absolutely love, which is called "A Familiar Quietness". It sounds like a cross between slow new wave and new age (Jeff Johnson in particular). It's practically instrumental with it's beautiful piano, synthesizer, the sound of water falling, and clean crisp electric guitar that expresses deep emotion. But buried underneath is the quite mutterings of a person talking. A perfect piece of music, though short. The rest of the album I have barely played. Some of the members of this band, would later team up with Jenny Gullen under the name Hoi Poloii.
Joy Electric -- I love synth pop, yet I'm not a big fan of this band. Too much bleeps and blops for my taste, but I've heard at least one tune from them that I like. They formed in the 90's.
Andy McCarroll & Moral Support -- They recorded at least one album called "Zionic Bonds". Unfortunately it doesn't pass the time very well. There's some good tunes, but some of it I find pretty painful on the ears (due to the production and overly dated quality).
Some other CCM bands that did new wave or new wave flavored music:
Mad at the World, Painted Orange, World Theater, Flock 14, The Imitators, and Code Of Ethics (first album is great).
Another group that is worth mentioning is The Call, a group outside the CCM subculture that had Christian or spiritual themes (just like U2 or The Alarm). Their first four albums from the early/mid 80's was mostly a mix of post punk or new wave with classic rock, sometimes having a touch of blues. Two songs you might like from this group is "Turn A Blind Eye" (very post punk) and "Even Now" (kinda sounds like The Smiths going new wave).
PS. A lot of the groups I mentioned can be found on You Tube. Too bad I can't do links yet.