....can a person legally (have in Possession, shooting at range, etc) a (semi automatic) "Bring-back" with no import markings or paperwork, or a "Sneak-Back" with well of course no documentation or markings?
There is no blanket answer: people do have in possession and shoot at ranges all manner of semi-auto "bring-back"s without import markings and with no or lost war trophy paperwork. With guns of certain ages, it's hard to tell what the origin was.
I would not want to get caught with a recent "sneak-back" that would require documentation or markings to be legit, especially knowing it was illegally snuck into the country. Bad juju.
A lot of M1 carbines and M1911 pistols were "sneak backs" concealed in duffle bags of returning GIs from WWII. A relative had a "bring back" SKS with proper paperwork as a war trophy. As vets of WWII, Korea, and VietNam die and heirs inherit their property, war trophy paperwork may be lost, blurring the line between illegal "sneak backs" and legal "bring backs" and guns that may have been bought on the commercial market back in the 1950s or 1960s.
In times past it was not uncommon for a GI to have a souvenir Luger or Nambu. Today the military takes a harder stance on what constitutes a proper "bring back".
But to the opening post, requiring import marks on foreign military (model, caliber, country of origin, importer) is a relatively recent regulation and appears to be dedicated to aiding in controlling current international export/import and in preventing illegal trafficking. (I have a 1950s import with the only added stamp country of origin.) There are a large number of legitimate curio and relic type military arms that never had current style importer marks, including some models now on the surplus market with full markings.
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IF the papered bring-back was full auto, the WWII paperwork could be recognized by the ATF to allow entry on the National Firearms Registry: one Tennessee congressman had his dad's WWII Reising SMG hung on his office wall for years, a "bring back" with paperwork signed by his dad's commanding officer. (That takes a lawyer familiar with the NFA work with the ATF. There are also procedures for surrending contraband without consequences but it requires being open and cooperative with the ATF, again best done with a lawyer familiar with the NFA.)