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

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

    def add_job(self, job_id: str, data: Any) -> None:
        self.jobs[job_id] = data
        self.retry_counts[job_id] = 0
        self.backoff_history[job_id] = []

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

        max_retries = 3
        backoff_delays = [1, 2, 4]
        
        # Initial attempt
        try:
            processor(self.jobs[job_id])
            return True
        except Exception:
            pass

        # Retry attempts
        for i in range(max_retries):
            delay = backoff_delays[i]
            self.backoff_history[job_id].append(delay)
            self.retry_counts[job_id] = i + 1
            
            # Simulate backoff delay tracking (no actual sleep)
            # time.sleep(delay)

            try:
                processor(self.jobs[job_id])
                return True
            except Exception:
                continue

        return False
```