On its own, it would be fine...if we were starting a team from scratch.
You can't brand a team and emphasize the Golden part, or make it a major point (as I assume we would do to differentiate from Philly/others)......but then dismiss the colour entirely and keep the EE logo. Not one of those teams refers to themselves or uses an acronym without their colour, as far as I know, and that's what we'd have to do for the EE logo to make any sense then.
And so you're either copying another major team name with Eagles only, or you're dismissing a classic logo and severing a major tie to history. Not a great alternative either way.
I don't know which I'd prefer - Eagles only, I guess - but I'd vote for Elks first.