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

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

    def add_job(self, job_id: str, data: Dict[str, Any]):
        self.jobs[job_id] = {
            "data": data,
            "retry_count": 0,
            "last_backoff": 0
        }

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

        job = self.jobs[job_id]
        max_retries = 3
        backoff_sequence = [1, 2, 4]  # seconds

        while True:
            try:
                processor(job["data"])
                job["retry_count"] = 0
                job["last_backoff"] = 0
                return True
            except Exception:
                job["retry_count"] += 1
                
                if job["retry_count"] > max_retries:
                    return False

                backoff_index = job["retry_count"] - 1
                delay = backoff_sequence[backoff_index]
                job["last_backoff"] = delay
                
                # Simulate backoff by tracking delay instead of sleeping
```