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

class JobQueue:
    def __init__(self):
        self.jobs: Dict[str, Any] = {}
        self.retry_counts: Dict[str, int] = {}
        self.backoff_delays: Dict[str, float] = {}
        self._delay_sequence = [1, 2, 4]

    def add_job(self, job_id: str, data: Any) -> None:
        self.jobs[job_id] = data
        self.retry_counts[job_id] = 0

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

        max_retries = 3
        for attempt in range(max_retries + 1):
            try:
                processor(self.jobs[job_id])
                self.retry_counts[job_id] = attempt
                return True
            except Exception:
                if attempt < max_retries:
                    delay = self._delay_sequence[attempt]
                    self.backoff_delays[job_id] = delay
                    self.retry_counts[job_id] = attempt + 1
                    # Simulated backoff: delay stored/tracked instead of time.sleep(delay)
                else:
                    return False
        return False
```