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

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

    def add_job(self, job_id: str, data: Dict[str, 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
        attempt = 0
        job_data = self.jobs[job_id]

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

        return False
```