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

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

    def add_job(self, job_id: str, data: Any) -> None:
        self.jobs[job_id] = data
        if job_id not in self.retry_counts:
            self.retry_counts[job_id] = 0

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

        job_data = self.jobs[job_id]
        retry_count = self.retry_counts.get(job_id, 0)
        max_retries = 3

        while True:
            try:
                processor(job_data)
                self.retry_counts[job_id] = 0
                return True
            except Exception:
                if retry_count < max_retries:
                    retry_count += 1
                    backoff = 2 ** (retry_count - 1)
                    self.backoff_delays[job_id] = backoff
                    self.retry_counts[job_id] = retry_count
                else:
                    return False
```