Upgrading from 10.2g to 11g by incrementals I know it's possible to generate a full rman backup in a 10.2g database, move it to another server containing 11g, restore it there and finally do an upgrade.

Since I have to do this to a large database and there are several things involved (apps, servers, network, etc), it could take me a few days and not only one night.

Could I make a full rman backup in 10.2g, restore it in 11g, upgrade, and in the next days go making incremental rman backups in 10g and restoring it in 11g, until we decide to shutdown 10g and use 11g in production. Something like a standby database, but in this case current database would be 10g and standby database would be 11g.
Once you upgrade the destination database to 11.2, you won't be able to apply archived logs (or incremental backups) from a 10.2 database.  So no, this won't work.

It is, on the other hand, often possible to use an actual standby database to perform a rolling upgrade.  You can create the 11.2 database as a logical standby of the 10.2 database, let the SQL apply process keep the databases in sync, and then switch over to the 11.2 database when you are ready to migrate.  In a similar vein, you could also use Streams between the 10.2 database and the 11.2 database to keep the data synchronized and then switch over when you're ready to migrate.