WBLDon,

in each workshop for the German hunting licence, some knowledge about Brenneke slugs
always is taught and a popular question in the examin is just yours! ;-)
And the answer is: yes, it's allowed to shoot slugs through full choked barrels.
On the German Brennecke site, they wrote "all Brennecke except for the "Opal" and "Super Sabot" are suitable for all kind of chokes. On their US site I cannot find this...!?
For your 16G Drilling they offer their "Classic" Brennecke and it will work.
I would be careful with other products, in Germany it has to be printed on the package.

Cheers,
Gunwolf