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

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
        self._retry_counts[job_id] = 0
        self._backoff_delays[job_id] = []

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

        max_retries = 3
        retries = 0
        job_data = self._jobs[job_id]

        while retries <= max_retries:
            try:
                processor(job_data)
                self._retry_counts[job_id] = retries
                self._backoff_delays[job_id] = []
                return True
            except Exception:
                retries += 1
                if retries > max_retries:
                    self._retry_counts[job_id] = retries
                    return False
                delay = 2 ** (retries - 1)
                self._backoff_delays[job_id].append(delay)
        return False
```