Backup policy for Oracle 11g database in non-archive mode
A partly online backup is certainly possible but switching to and back from archivelog mode needs downtime. As an alternative you could run in regular archivelog mode and trash the generated archived log files, until you run a backup.

For the backup to be recoverable it is important that it has ALL archived log files that were generated during the backup. End the backup with a log switch and also include those archives in the backup.

You must see this kind of backup as partially online. It does allow you to restore to the point in time where the backup completed, not to any other point in time. Very similar to regular offline backups, only, taken online. It saves downtime.

Why do you want this? This is a lot of effort just to safe maybe 10G of archive storage per day. It also introduces an extra error source and many dba's won't be able to work with this and expect to have all archives. My advice would be to keep it regular online backups, with regular archived log backups and keep things simple.