My desk broke while testing this. This is your fault.
Also, sorry for taking so long to do this. I meant to get it done sooner, but I had to go somewhere for the weekend, so I wasn't able to, and then I completely forgot about it for a while.
Gen 3 (Tested in Emerald):
Static: Electric type Pokemon appeared 4/5 times. (Tested on Route 110, if that matters.)
Magnet Pull: Steel type Pokemon (Skarmory, in this situation) appeared 3/5 times. (Tested on Route 113.)
Cute Charm: When having female Jigglypuff at the front of the party, encountered Jigglypuff were male 5/5 times. (Tested on Route 115.)
Synchronize: When having a Quiet Natu at the front of the party, encountered and caught Pokemon had a Quiet Nature 3/5 times.
Vital Spirit/Hustle/Pressure: The levels Zubat in Meteor Falls (While surfing) appeared at were 35, 11, 35, 33, and 35.
Keen Eye/Intimidate: The levels Wingull on Route 107 (While surfing, while the party leader was a level 26 Wingull.) appeared at were 29, 21, 26, 24, and 16.
Gen 4 (Tested in HeartGold):
Static: Electric type Pokemon (Magnemite, in this situation.) appeared 1/5 times. (Tested on Route 6.)
Magnet Pull: Steel type Pokemon (Magnemite, in this situation.) appeared 2/5 times. (Tested on Route 6.)
Cute Charm: When having a male Jigglypuff at the front of the party, encountered Machop were female 4/5 times.
Synchronize: When having a Docile Natu at the front of the party, encountered and caught Pokemon had a Docile Nature 2/5 times.
Vital Spirit/Hustle/Pressure: The levels Poliwag on Route 31 (While surfing) appeared at were 25, 22, 18, 17, and 25.
Keen Eye/Intimidate: The levels of Poliwag on Route 44 (While surfing, while the party leader was a level 30 Gyarados.) appeared at were 23, 15, 24, 27, and 20.
Gen 5 (Tested in White 2):
Static: Electric type Pokemon appeared 1/5 times. (Tested at Floccesy Ranch.)
Magnet Pull: Steel type Pokemon (Skarmory, in this situation) appeared 3/5 times. (Tested at Reversal Mountain.)
Cute Charm: When having a female Jigglypuff at the front of the party, encountered Minccino were male 4/5 times.
Synchronize: When having an Adamant Munna at the front of the party, encountered and caught Pokemon had an Adamant Nature 2/5 times.
Vital Spirit/Hustle/Pressure: The levels Basculin at Village Bridge appeared at were 40, 30, 26, 40, and 38.
Keen Eye/Intimidate: The levels in Zubat Castelia Sewers (While the party leader was a level 20 Sandile.) appeared at were 16, 16, 14, 15, and 17.
Gen 6 (Y and Omega Ruby):
Static (Tested in Y): Electric type Pokemon (Pikachu, in this situation) appeared 1/5 times. (Tested on Route 3.)
Magnet Pull (Tested in Omega Ruby): Steel type Pokemon (Skarmory, in this situation) appeared 1/5 times. (Tested on Route 113.)
Cute Charm (Tested in Y): When having a female Skitty at the front of the party, encountered Liteo were male 4/5 times.
Synchronize (Tested in Y): When having a Modest Gardevoir at the front of the party, encountered and caught Pokemon had a Modest nature 1/5 times. I would also like to add that I wasn't paying attention to how many Pokemon I had caught, so I caught a sixth Pokemon, and it was also Modest.
Vital Spirit/Hustle/Pressure: The levels Pelipper on Route 124 (While the party leader was a level 36 Weavile.) appeared at were 25, 25, 35, 25, and 35.
Keen Eye/Intimidate: The levels Pelipper on Route 124 (While the party leader was a level 37 Arbok.) appeared at were 25, 25, 25, 25, and 25
Conclusion: In Gen 3, all overworld abilities work when a Pokemon is encountered with Sweet Scent. In Gen 4, Magnet Pull and Static seem to not work outside of battle with Sweet Scent. In Gen 5, Static doesn't seem to work outside of battle with Sweet Scent. In Gen 6, Magnet Pull and Static seem to not work outside of battle with Sweet Scent.
Also, if there's any specific area you would like me to test these in or an ability you would like for me to test again, let me know and I will, if possible.
Still trying to get Pressure and Intimidate tested.