```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, list] = {}

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

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

        max_retries = 3
        backoff_sequence = [1, 2, 4]
        current_retries = self.retry_counts.get(job_id, 0)

        for attempt in range(max_retries + 1):
            try:
                processor(self.jobs[job_id])
                self.retry_counts[job_id] = current_retries + attempt
                return True
            except Exception:
                if attempt < max_retries:
                    self.backoff_delays.setdefault(job_id, []).append(backoff_sequence[attempt])
                else:
                    self.retry_counts[job_id] = current_retries + attempt
                    return False
        return False
```