Is it possible to run CodeIgniter within a TideSDK App?
Looks like TideSDK does support PHP, so there is no reason why it would not.
One caveat, though, is that TideSDK does not seem to support MySQL. If you need to take advantage of database functionality, you would need another solution. Luckily, a CodeIgnider SQLite module is available, which should take care of that problem. (SQLite is a self-contained SQL database system, effectively allowing you embed a database in a file.)