I have 7 recruits on my controlled battlefield. Enemy Astral Heron with 7 might moves to my battlefield. I play Imperial Decree. Would the Heron be able to eliminate 7 of my recruits?

Yes — with Imperial Decree out, the Heron's 7 Might kills all 7 of your recruits, but the Heron dies in the same exchange.

Damage is assigned and then dealt simultaneously (CR 467.2.c). Your Recruits are 1 Might each, so 1 damage is lethal to one of them, and CR 467.2.c.4 stops the attacker from piling extra damage onto a single Recruit while other units remain — the 7 damage has to go 1 to each of the seven (so it can't "save" damage by only hitting a few). Coming back the other way, your seven Recruits sum to 7 Might, which is exactly lethal on the 7-Might Heron, so it dies too — and Decree would kill it on any damage at all anyway.

Worth knowing: Imperial Decree hurts you here rather than helping, since your Recruits were dying to lethal damage regardless and the only extra thing it does is guarantee the Heron dies (it already would). With all units dead, this is a "No Result" combat and the battlefield has no units remaining, so it becomes Uncontrolled afterward (CR 468.3.d, 468.5.b) — you don't keep it.