Is a split or break in a plywood seat repairable?  

Maybe
Plywood is not easy to repair. But it might be possible. You've got to get glue deep into the delamination. Possibly use a syringe. If there are unglued areas past your glued area they will become the new weak spots and send the delaminations deeper into the plywood. Once glued then you have to clamp it really tight. A thick area of dried glue between the layers is brittle and will rebreak, so clamp it beyond what you think necessary, and then add some more clamps. You might also need to spend time upfront planning shaped blocks you can clamp against the piece to distribute the force over a wider area. When you're done clamping, you want it to look like you've squeezed out all the glue you put in.
Good luck.
Other advice form the forum:
http://www.designaddict.com/design_addict/forums/index.cfm/fuseaction/th...
http://www.designaddict.com/design_addict/forums/index.cfm/fuseaction/th...

Anything is possible.
The difficult part is deciding which level of perfection or imperfection is acceptable and whether or not the repair is worth the expense and effort.

The poster is
unclear on the nature of the defect. I assume it is a delamination of some sort, and not a break through several or all of the plies (a doubtful situation, given the nature of the material and the comment that the damage may have resulting from careless stacking). A 1" "split" in a 1/2" (?) thick plywood seat seems unlikely to me to be a structurally hazardous condition. A picture would help, obviously.

Thank you
Thanks for a very helpful reply. I wouldn't do the repair myself but I would get a carpenter / wood worker to repair it, but before that I wanted to know if it was even worth repairing. I don't have a flickr account so I haven't uploaded any photos but I went to photograph the chairs today and discovered that they have all had some repair to the sides. On closer inspection the side of the seat has been a cut into - they have cut away a 1 inch piece of the original wood and rejoined a replacement bit of wood into the side (like a jigsaw puzzle). So what I thought were splits in the wood is actually the replacement wood piece coming away.
Having read the other links I don't think this could ever be repaired strong enough to not break off again. I love these chairs but if I can't sit on them worrying the side will break off again then it seems a waste of money.
I was deliberating about getting some jacobsen chairs instead but having read the links that they are prone to breaking I'm stumped. I have a thing for plywood chairs and didn't know how fragile they are.
Any suggestions on a robust 50s dining chair? Hillestak Robin Day is another fave but I think they would need regluing over time right?!

A robust dining chair...
Well if you want robust, almost all the Moller designs are robust and well-built. Erick Buck chairs are also reasonably robust, except for the plywood inside the upholstered bits, but being inside upholstery give you options for fixing it.
Those are the first two that come to mind.