You do not put *database* into backup mode, you put *tablespaces* or *datafiles* in backup mode! And you can do this in all versions at least since Oracle7.

But as far as stanby database and the backup mode is concerned, the question is irrelevant. If you put your standby database out of recovery mode, then the database is either:
- closed, nomounted or mounted
- opened read-only

In any of those states, the database is as good as "in backup mode", and you can safely perform a backup the same way as you would perform cold backup. No need (nor ability) to use BEGIN BACKUP and END BACKUP options with standby.

P.S.
Of course, we are talking strictly about physical standby here. With logical standby it's another story.