The short answer to that is no – that is, you paying a large amount of money to the OC will just be a forward payment on your levies, it has nothing to do with works that may be required to fix the garage, and it doesn’t make you exempt from future levies, where the amount you have paid is less than the amount that might be owing at any given time.
Your key concern seems to be that you want the garage ceiling fixed as soon as possible. The OC has a duty to repair and maintain the common property. So I suggest you write to the Committee advising that your garage ceiling requires work, in line with the other works, and that this needs to be done as a priority.
If the Committee stalls or delays doing the work then you will have to consider whether to escalate the issue. Another approach if they do stall is to offer to pay for the works yourself, but that they must reimburse you, or the amount is reflected as a credit against your levies. However to do that, you would have to make sure that the Committee and/or OC resolve that the works must be done, to make it clear that it is an OC responsibility.
It’s not clear from your post whether it is the special levy that has been set or the works that have been completed. If the works have not been completed then it would be easy to vary those works to include your garage ceiling.