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.
This MOS (Metalink) note discusses restores between different versions:
Frequently Asked Questions about Restoring Or Duplicating Between Different Versions And Platforms [ID 369644.1]
It is very likely that you cannot apply 10g incremental backup to an upgraded (to 11g) database. The upgrade changes data in the SYSTEM tablespace, so I seriously doubt you can apply incremental after that.
Something like a standby database
Way to go – make a real standby (10G) on the new server. Install the 11g new software and when the time comes - upgrade.
The timing of the upgrade does not depend on the size of the DB, but rather on the number of objects in it. In most cases, the update would take only a few hours, but you should test to find out the timing in your case.
How big is the database ? How much downtime can you afford ?
AFAIK, you cannot restore incremental RMAN backups in the manner you have suggested.
One possible option is to use GoldenGate (licensed separately) to minimize downtime for your upgrade.