Not quite.
http://na.finalfantasyxiv.com/a_real...ent?threats_02In subjugating Ala Mhigo, van Baelsar employed subterfuge to stoke the fires of civil unrest, a masterstroke which led to the nation’s capture without the need for a protracted siege. However, the unanticipated appearance of a primal shortly thereafter prompted the Empire to halt the legion’s advance.
This is 1557. In 1562 is when Midgardsormr appears during Gaius' attempt at conquering Mor Dhona. The timeline, basically, should be: Fall of Ala Mhigo -> primal! -> Let's wait a second -> okay we got the Agrius -> Midgardsormr! -> LOTS OF PRIMALS!? -> Let's wait a second -> Meteor Project.
At the very least, for all of 1.0, the Battle of Silvertear and the primal appearance (stopping the advance on Eorzea) are treated as wholly separate occurrences. Likewise we know the Empire knew of primals before Silvertear Skies; after all, they had encountered them in Othard. Having known what a Primal was (roughly) they would've known Midgardsormr wasn't a Primal simply because his corpse didn't dissipate into aether. Furthermore, Minfilia's father, Warburton dies attempting to smuggle Imperial knowledge on Primals to Eorzea.
As I noted previously, this primal appearance immediately post-Ala Mhigo has quietly fallen into obscurity after 2.0's pre-release material so it's possible it's been removed from canon. If it is supposed to be Midgardsormr it's either a retcon or we have to accept that Garlemald is smart enough to realize Silvertear Lake is the center of aetherial confluence on Hydaelyn but dumb enough not to know that an aetherial deiform dissipates when killed.
Furthermore, the probable final time this Primal is mentioned is Gamer Escape's interview with Koji Fox (Fernehalwes):
https://gamerescape.com/2014/10/22/f...pher-koji-fox/MCKF: [laughs] Yeah, so the primal that made them halt their advance, I still can’t answer that.
F: Wow.
A: And it’s been so long, almost as long as Ishgard! I’m excited to hear about it.
MCKF: It’s a ways off, but you’ll find out someday. It’s not something we’ll keep quiet about. They have their long-term plan. Before A Realm Reborn was released, they already had plans beyond 2.4.