Short answer: Yes. Pre-contract application is faster (20 days) and recommended.
Yes, and you should. It is called a pre-contract application. It tells you exactly how much grant money you qualify for. Then when you find a house, you just update the application with the address. Pre-approval takes up to 20 working days. Post-contract takes up to 50.
Pre Contract: Apply now, get approved in 20 days
Find House: Find house in month 2
Update Application: Add address, approved in 5 days
Total Time: ~25 working days