Basic Training, Page 27. Weapon Familiarization.
Further, page 13-14 says you can train to the lower of skill level -1 of the skill or of instruction. It also says instruction 1 is the minimum to conduct any training at all.
The math this produces is 1-1=0, thus Instructor 1's can only teach level 0. But the fact that they can teach level 0 in firearms is explicit on page 27, tho' not worded as such.
Therefore, level 0 skills, at least in firearms, may be taught. Given the rules, there is no benefit to teaching level 0 instead of level 1 IF the isntructor is capable, and the student is not maxed out on skill levels.
TTB page 29 states several skills are appropriate for level 0 use (See default skills); the limit on skills (Maximum Skills, ibid.) states level 0 skills don't count against the limit.
Note that Bk1, printing 12, lacks the limit on skills, and reference to level 0, and calls basic weapons expertise a level of "1/2"...
It's tenuous, but present, that based upon TTB and Bk4, one can use instruction to train level 0 skills, and possible that it includes skills other than weapons.
Further, the implication of the section on default skills on page 29 of the Traveller Book implies the unskilled penalty is automatic failure.