This is entirely possible, but a few things make me thing otherwise.
Moving with the assumption that the gods are the ones who sealed Zodiark (based on Ivalice lore and... really, who else could have done it?) I would be interested to know what Midgardsormr's role in it was, if any. There seems to be an awful lot of similarities between the seal in Silver Tear Lake and Zodiark. However, there are some key differences.
Firstly, the sheer amount of destruction that the Agrias did and that which the Ascions attempt are hardly comparable. It would seem that whatever seals bind Zodiark are substantially stronger and require much larger destructive forces.
Also, the type of destruction and it's target seem less focused. The Ascions don't seem to have a targeted location for the destruction they wish to cause. They encourage primals to pop up all over the land, and Bahamut's calamity leveled the Carteneu Flats as well as the outlying areas, not silver tear. This leads me to believe that whatever seals bind Zodiark may be similar to those which were in effect within the lake, but not the same. They seem to be more of a cosmic nature, as the Ascions goals are more involved with "balance" and general chaos.
The fact that Zodiark is being played out to be Hydaelyn's opposite also makes me believe that he exists on a more cosmic plane. As Hydaelyin is often represented in cutscenes as the Mother Crystal floating in space, it's more than likely that Zodiark exists in a similar fashion. The question is, where? My first instinct was to say somewhere in The Void, as it seems to be the closest place we've been in the game that acts as the opposite to Hydaelyin's domain. That being said a more radical thought has struck me...
Assuming that Zodiark was sealed in a similar fashion to the Primals (in a crystal, or using a crystal as a seal), I find it interesting that Hydaelyn herself is represented by a massive crystal. This presents two possibilities to me. The first is that the "Mother Crystal" we see when speaking to Hydaelyn is actually the prison that was fashioned for Zodiark. It's possible that Zodiark's powers were so great that Hydaelyn herself had to use her own body as a means of subduing him. This would mean that the reason the Asicions are attempting to cause so much destruction to Hydaelyn's world is to break Hydaelyn herself. They want to cause Hydaelyn enough pain to make her crack and release their god. Scary thought.
The second possibility is that Hydaelyn's representation reflects Zodiarks (as they are opposites). This would imply that Hydaelyn is also subdued within her own confinement. In effect, both her and Zodiark are sealed to some extent. It would explain why she seems to lack character and is extremely limited in her own interactions with her world. She relies on her champions and echo users to do things for her, similar to the way that Zodiark relies on Ascions. This theory would also explain Elidibus's previous absence.
When he first shows up he makes a comment (which I can't quite remember at the moment) about how something has changed in his absence. Where was he? It seems likely that Elidibus was with Zodiark, speaking with him in broken dialogue much the same way Hydaelyn speaks with us. This would imply that Zodiark is capable of communicating on some level into our physical world. Presumably he has only spoken to Elidabus, but who knows? Maybe he'll speak to us one day? Maybe he should be able to, because of the Echo, but cannot because Hydaelyn has claimed us as her own (similar to the way a Primal tempers a subject) and is preventing us from hearing his voice?
This is all purely speculative, obviously, but very interesting in terms of what may or may not be happening in our little corner of the galaxy.