There are several issues here:
1. Long hose. This should not be a problem, though some instructors still insist on donation of the secondary.
2. Necklace secondary. This can be a problem with skills like equipment doff and dons and exchanges. There are some instructors that have a problem with the idea of securing anything "solid" around your neck, so make sure the necklace is "break-away."
3. Snorkel. Agency standards require that the students be "equipped" with a snorkel. Reading that as "in you gear bag" or "in your pocket" is, I fell, also an issue. "Equipped" (to me) means on your mask strap. That said, most of the concern over wearing a snorkel comes from three things: 1) Potential entanglement. 2) Fouling on the long hose during deployment, and 3) Not being of any use. If a snorkel is worn (positioned) properly, items 1 and 2 are, with a small amount of care, not an issue. As to 3) that depends on how you dive. Old school says, "never waste air on things like surface swims or kelp crawls," new school says, "buy a bigger tank." I guess it depends on where you are coming from.
4. An issue you did not raise is clipping off your SPG. Some instructors feel that the entanglement potential of any "hard loop" that ou create is a safety issue, so the teach putting your SPG under your tank in the small of your back (where it will usually stay).
5. Last but not least, is the question of a crotch strap and putting your weightbelt on before you buckle your BP/W straps. I feel that your weightbelt should go on last so that it can be ditched, there is some controversy on this topic.