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

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

    def add_job(self, job_id: str, data: Any) -> None:
        self.jobs[job_id] = {
            'data': data,
            'retry_count': 0,
            'last_backoff': 0
        }

    def process_job(self, job_id: str, processor: Callable) -> bool:
        if job_id not in self.jobs:
            return False

        job = self.jobs[job_id]
        retry_count = job.get('retry_count', 0)
        max_retries = 3

        while retry_count <= max_retries:
            try:
                processor(job['data'])
                job['retry_count'] = 0
                return True
            except Exception:
                retry_count += 1
                job['retry_count'] = retry_count

                if retry_count > max_retries:
                    return False

                backoff = 2 ** (retry_count - 1)
                job['last_backoff'] = backoff

        return False
```