Yes, you can get regular loot this way. I've seen a screenshot of someone getting it in the middle of the desert irrc, but it wasn't me and I can't find it.
Your character's location on the map does not affect your loot. What matters is your participation in the fight. Regarding Scarlett Etzel specifically, you may not be eligible for the full loot if your participation is very low. This can happen if you only hit Scarlett once and barely take any damage, and the player that stays with it takes some damage and deals more damage. Participation is proportional to the contribution (damage taken/dealt) of all players during the fight.
If you only get a green gem, energy bar and some platinum coins then you probably didn't get enough participation. If you also got other items such as terra set items and potions then you got the regular lot and could have dropped a Cobra Item.
It's actually easy to test it out. Because of how Scarlett is killed, if a player tanks/attacks it in melee range for some turns (10+) he/she will most likely get all the participation for himself and no one else will get full loot.