Wanna throw out an incredibly minor correction here: not sure if it was in 656 or 657, but on the podcast it's mentioned in a throwaway sentence how Smash Bros. Melee saved Fire Emblem after the SNES. That's not the full story, though.
Fire Emblem 6: The Binding Blade (starring Roy, who was in Smash Melee) was what came out of the scrapped N64 game (formerly titled Fire Emblem: Maiden of Darkness) that got repurposed to release on GBA in March 2002 in Japan. I imagine the long development cycle is why Sakurai got the heads-up about Roy and crammed him in Smash Melee. Note that Melee
precedes FE6 in Japan by ~4 months.
Fire Emblem 7: The Blazing Blade was
already planned, but took longer to come out due to the protracted dev cycle of part 6. Note how Fire Emblem 7 is a prequel to 6, set in the same world. That delay between 6 and 7 allowed the game to get localised, and it would be the first in the series to release in the West (simply as
Fire Emblem on GBA).
That
decision to localise it was spurred by two reasons: the reception of Marth and Roy in Smash Melee, but also the success of
Advance Wars during the GBA launch in the West. In some ways, this was simply the earliest project Intelligent Systems could launch to follow-up Advance Wars with. (It's my personal theory this is also why FE8: The Sacred Stones was rushed to market on GBA too; the success of Advance Wars and FE7 proved turn-based combat sold on handhelds in the West.)
So yes, this is some real hair splitting, but technically I think that if Smash Melee never existed, at the very least Fire Emblem 6 and 7 would still have released. They would just have stayed Japan-only, as the series had been until then.
Did Smash Melee
launch the series in the West? Partially yes, although Advance Wars proved the viability of turn based strategy on handhelds in the West too. I do definitely think Smash greatly contributed to the
localisation of the series, and yeah they probably would've never greenlit two moneysinks like Path of Radiance and Radiant Dawn on GC/Wii without Melee bringing these characters into the GameCube ecosphere... But I think the series would probably have survived on handhelds in Japan regardless.
Sorry for sounding so nitpicky, but RFN is usually great with minutiae like this, so I figured I'd chuck some extra nuance in the comments.