No, the BLE identities of these tags are currently practically indistinguishable from original tags, and could be made completely identical if necessary. In fact, changing the device's MAC address is part of the specification. What they could block, is the method used by these projects to fetch encrypted location reports. However, the original OpenHaystack project (this one) needs to run on macOS and lets the system handle account authentication, so it's unlikely to get blocked any time soon.

If I remember correctly, Apple was supposed to openly accept and encourage others to leverage their network and make more “AirTag” capable devices.