That is a real pretty cover tuck you put on that. I wouldn't count on it adding any strength.
These ropes are "core-dependent" double braid, which means that 100% of the strength is in the core. The cover only serves to protect the core. That being said, a while back we had a member who was load testing his splices, and doing some real neat work. As I recall, Moray tested just the cover of Bee Line to exceed the rated strength of the entire rope.
Where your tucked cover distorts the natural curve of the eye splice will be a weakened part of the splice. Virtually all splices are weakest at the end of the taper, where the single rope is carrying the entire load but is bent over the buried taper. I think your tucked cover is very tidy and neat, but I think it is an illusion to think that it might add any strength. For starters, it isn't being pulled on from the eye, so it isn't going to carry any of the load.
I think it might do an outstanding job of keeping the eye open for 'biner insertion.