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

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

    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
        backoff = 1
        delays = []

        try:
            processor(self.jobs[job_id])
            self.retry_counts[job_id] = retries
            self.backoff_delays[job_id] = delays
            return True
        except Exception:
            pass

        while retries < max_retries:
            retries += 1
            delays.append(backoff)
            backoff *= 2
            try:
                processor(self.jobs[job_id])
                self.retry_counts[job_id] = retries
                self.backoff_delays[job_id] = delays
                return True
            except Exception:
                continue

        self.retry_counts[job_id] = retries
        self.backoff_delays[job_id] = delays
        return False
```