So yeah. That's my idea on how Rainbow Dash survived Fallout: Equestria and her descendants are going to help Gryphus curbstomp the Pegasus Enclave before conquering Equestria in the name of the Emperor.
It's a good idea, but it does conflict with some parts of the Fallout Equestria story that I don't want to spoil that require Rainbow Dash to do some actions that help the main story. My suggestion would be to merge in the author's headcanon of Rainbow Dash's fate with a reason as for why Gilda became a mercenary.
Gilda is the leader of the Griffons who refused to follow the call, either because they didn't want to leave the homes and livelihoods they'd built or because they think the Emperor's snapped from his injuries and Gryphus might end up more dangerous than Equestria. Gilda's reasoning for staying is her friendship with Dash and newly appointed head of the Ministry of Awesome (fun fact: Dash named her ministry before she got around to figuring out what it was supposed to do) hires Gilda as a 'consultant' with over the period of the war (the Great War is described as a decades-long conflict) it evolves into a mercenary company of non-ponies, mostly Griffons, fighting for Equestria for a whole lot of bits to support the exiled Griffons.
However, after the invention of Megaspells (Fallout Equestria's nuclear equivalent, an arcane matrix that enhances any spell put into it originally for healing purposes... but ideas were had), the more military minded Griffons realise what it means and start working with Stable-Tech to build their own Stable to house non-ponies with Gilda keeping it a secret from Dash as she doesn't want to look weak in front of her best friend.
The Pegasus Enclave hiring Gilda to kill Rainbow Dash wasn't their first choice, but after several more subtle attempt failed, they went to the one who knew her fighting style best and hadn't been trained by her. Gilda takes the job for two reason, firstly the Enclave offers a lot of money and while the Stable is done, it could always use more equipment and secondly she knows Dash's Loyalty means even if she could reach it to a Stable, Dash would simply use the opportunity to save other ponies instead of saving herself. Not wanting her best friend to die horribly from fire and radiation poisoning, Gilda decides to give Dash a less painful death (in canon she respects Dash entertain her last request to sing the Junior Speedsters song with her one last time before they battle).
The battle is a draw with the Last Day interrupting it, Dash flies off to be a hero and Gilda knowing that it would be impossible to stop her, hurries back to the Stable to look out for her people, living out the remainder of her life as its first Overseer. Rainbow does her thing and gets Ghoulifed, retaining her sanity by donning the costume of Mare-Do-Well and acting as a vigilante fighting across the Wasteland protecting the weak and trying to redeem herself for helping form the Enclave and failing to stop the war.
Story wise this gives us a separate 'Wasteland' Griffon faction who perhaps just emerged from their Stable and keeps Rainbow around as the FoE equivalent of the mysterious stranger.