Is it possible? Yes. However, putting aside the fact that copying a binary poses a security risk, you should not be storing anything inside the /tmp/ folder. As the name suggests, it is a temporary folder and is not persistent storage. It gets cleared on a reboot
So, the potential workarounds are:
Containerize the function app. You can create a custom container and deploy your function inside that, giving you full control over the runtime environment
Continue to copy the binary to /tmp/
Use a premium or dedicated plan instead of consumption plan. The filesystem for these plans are writable and persistent.