Oracle Standby Database - Archivelog GAP
Assuming you mean that the database is "missing" logs from P->R, and that your primary database no longer has those logs either, then the answer is that you'll have a functional database (upon standby activation as a primary) but you will be missing data from P-> the Activation point. 

The thing to remember here is that your standby is only as good as your last archive log that was fully applied. Without intervention on your part, your standby database is essentially frozen in time, and will never advance.

If you're missing archive logs, and they are truly unrecoverable (did you check storage backups? Backups to tape?), then your standby, IMO, is worthless as a production level standby. You, and your business, may have a different opinion based on your usage of the database in question.

But if this was truly a production level standby database that is meant to take over for production in a disaster scenario, personally, I would rebuild the standby immediately.