```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, "backoff_delay": 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]
        backoff_delays = [1, 2, 4]

        try:
            processor(job["data"])
            return True
        except Exception:
            pass

        for i in range(3):
            job["backoff_delay"] = backoff_delays[i]
            job["retry_count"] += 1
            try:
                processor(job["data"])
                return True
            except Exception:
                pass

        return False
```