Vision or not, Sonic or somebody in the game would've lost it to Chaos anyway.

Given how often Sonic lost the chaos emeralds every time by some contrivance, then no.

Could Sonic have reached the last Chaos Emerald before Chaos if Tikal hadn't stopped him with that final vision?.

Sonic X has Eggman specifically accuse Lily/Birdie of stealing the Chaos Emerald from him, suggesting it may have taken an Emerald he had already obtained from his lair during its escape.

The three birds find it, keep it, and then two of them get kidnapped by Eggman and the other one gets chased by Zero until it runs into Amy.

The Chaos Emerald is a shiny object, birds like shinies, and the Chaos Emeralds are hidden across the 'world' anyway.

As for the Chaos Emerald inside.*Le-Shrug* Birdie's family probably got the locket and took a family picture to put inside it just like any human or anthro would.

It's been shown that all animals in the Sonic World are higher functioning than what would be expected of normal animals.

Sonic adventure mystic ruins