Dark Samus shows they can have extremely different animations, but Echo Fighters draw almost entirely from one character. Chrom's unique Up-Special is entirely his own move, not actually ripped from Ike, but the point does stand that at least one Special attack can be very different. Basically, if Celica is an Echo Fighter, she absolutely has to fit cleanly next to another FE character and play almost identically, to the point where you could almost consider her an alternate costume with slightly different properties and animations. The animations still have to result in logically the same hitboxes or types of sword swings, though, as we see Dark Samus and Samus' missiles and Charge Shots have virtually identical height when fired, despite the slightly different animations (ex. Dark Samus adopts a "firing from the hip" posture with her charged shot and missiles, Samus fires with a more professional position, but both bend their knees so their shots have the same height). Note that Dark Samus' dash attack, despite a very different animation, is still a shoulder tackle. Also, note that several of Dark Samus' attacks remain identical to Samus, including up, down, and back aerials, as well as up-special.
So, in summary, if Celica is an Echo Fighter of Robin, she can have at least one move of her own, but her stats must remain identical, her animations, though they can be quite different, can't be totally overhauled for the attacks, and most of her attacks and properties have to be the same as Robin's, which means that Celica's swordplay would be unrefined, and while she doesn't have to use tomes and can use her own animations for casting her attacks, most of them still have to be the same overall as Robin's.
Corrin simply doesn't work as the base for an Echo Fighter as their dragon powers are entirely unique to them, and making anyone an Echo of them would result in them gaining transforming lance-arms and mouth-hands, not to mention the few attacks Corrin has where they go full-on dragon. Marth has the same problems as Robin in the opposite direction, as while Celica's swordplay is refined and she has been a Marth clone before, we only know for sure that she can have one unique move, which would have to be a magic attack, but otherwise she's identical to him, and as I've said before, I highly doubt Sakurai would include a second Echo Fighter for Marth, for MANY reasons.
If Celica gets in, at worst she's a semiclone. Most likely, she'll be completely unique.