I think it should work in a cookie or persisted - b/c both apps use the same domain and secret, they can share the cookie/session.
I've done projects like this twice. Once where we synched the data, and ran in parallel.
That was a nightmare - the complexity of the transformations created many issues, and latency.
I am not saying don't go the synch route, but do be aware of the issues involved, and how much work it will be. If it is a simple db, with only smaller differences in schemas, and simpler synch logic, this can work I believe, but ours did not have those characteristics.
More lately, moving a java app to rails, much of the point was to make major schema changes and clean/transform data in ways that would be very hard to synch in real time. We opted to not run in parallel, and migrate the data and flip the switch when the new app was ready. Not in the cards for you in seems, but that was the best option for us. We made all our migration scripts as ruby code, sql, and rake tasks, and wrote tests to make sure the data looked right after each step.
Now, if you do decide to ride on the existing db you have some excellent tools.
AR has a lot of flexibility with aliasing columns, setting the primary key column, and the table name, to allow you to operate even on non-default AR tables. You can also add columns (with defaults or triggers to make the old app work) without too much pain, so if a surrogate key or type column is needed, not a big big deal.
For keeping the same db but making tables more rails-flavored, views can be helpful.
For example, you can use them to break up or combine tables, or rename columns.
Now, they are read-only (most of the time, depends on the dbms), so updates will need special handling - but you can end up hiding most of this complexity in your models and db (with views/stored procs), and leave the rest of your app clean.
Then, after you have closed down the old app, you can get rid of the tech debt by actually updating the old schema, and simplifying the models back to default behavior - or just leave it be, in cases where it is cosmetic, and stable (depends on how much of a purist you are, and how much time you have to throw at such idealism).
This is an old prez related to this, but then again, it is an old problem :)
Hope that helps,
- Andrew