```python
from typing import Callable, Dict, Any

class JobQueue:
    def __init__(self):
        self.jobs: Dict[str, Any] = {}
        self.job_metadata: Dict[str, Dict[str, Any]] = {}

    def add_job(self, job_id: str, data: Dict[str, Any]) -> None:
        self.jobs[job_id] = data
        self.job_metadata[job_id] = {"retry_count": 0, "backoff_delays": []}

    def process_job(self, job_id: str, processor: Callable) -> bool:
        if job_id not in self.jobs:
            return False
        
        data = self.jobs[job_id]
        metadata = self.job_metadata[job_id]
        
        max_retries = 3
        
        for attempt in range(max_retries + 1):
            try:
                processor(data)
                metadata["retry_count"] = 0
                return True
            except Exception:
                metadata["retry_count"] = attempt + 1
                
                if attempt < max_retries:
                    delay = 2 ** attempt
                    metadata["backoff_delays"].append(delay)
                else:
                    return False
        
        return False
```