Jet A1,
Go for it!
If you can gain any kind of operational experience before getting a flying job, you will benefit from it. As mentioned earlier in the thread you will find it difficult to persuade an Ops manager to take on someone who could be gone tomorrow. 10 years ago someone took a risk on me, and it was the best move I ever made. I can only suggest that you write to every chief pilot, explain your position, and ask if you could spend a week as "work experience". Certainly most chief pilots would be impressed with your attitude.