Signing the message in this way will enhance privacy as long as you are offline.
The problem lies in broadcasting the transaction. If you broadcast all of them using the same server, the same IP, and the same device, the transactions may be linked.
Do not forget that many companies that analyze the blockchain link identity with some indirect methods, such as:
- Searching in Blockchain Explorer: Searching in Navigators might be a bad option.
- Connecting inputs and outputs: It doesn't matter how the transaction is broadcast as much as how you got the money to whomever you want to send it to, in one blister or another we will reach an address whose identity has been verified.