SQL Server 2016 does allow far more minimally-logged INSERTs to an existing clustered index than any earlier version of SQL.
And, in some instances at least, it does allow simultaneous INSERTs to the index.
Whether or not those INSERTs can be parallelized, as I said, I'm not sure. If, for example, the data was coming from an existing index already sorted in the correct order, and SQL "knew" that, I think it should be possible for SQL do INSERTs to other table from that source index in parallel.
But, when SQL has had to sort random data as the input source, I'd be surprised if SQL was able to do parallel INSERTs of that just-sorted data (note that I'm not saying it can't happen, I'm saying I'd be surprised at it).
SQL DBA,SQL Server MVP(07, 08, 09) Prosecutor James Blackburn, in closing argument in the Fatal Vision murders trial: "If in the future, you should cry a tear, cry one for them [the murder victims]. If in the future, you should say a prayer, say one for them. And if in the future, you should light a candle, light one for them."