```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] = {}

    def add_job(self, job_id: str, data: Dict[str, Any]):
        self.jobs[job_id] = data
        self.retry_counts[job_id] = 0

    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]
        retry_count = self.retry_counts[job_id]
        
        # Attempt initial run + retries
        while retry_count <= max_retries:
            try:
                processor(self.jobs[job_id])
                return True
            except Exception:
                if retry_count < max_retries:
                    retry_count += 1
                    self.retry_counts[job_id] = retry_count
                    # Track backoff delay without sleeping
                    delay = backoff_delays[retry_count - 1]
                else:
                    # All retries exhausted
                    self.retry_counts[job_id] = max_retries + 1
                    return False
        
        return False
```