The short answer to this is: no.
The AutoEntry Sync App should only ever be installed on one device. We would advise, where possible, having this installed on the device where your Sage/QBD data is stored.
The connection between AutoEntry and Sage 50/QBD will be through the device that the integration was initially set up on. As long as the sync app service is running on this device, publishing/data syncing can be done on any other computer.
If there are any additional installations of the sync app, these will show the status of the integrations, however will not create an active connection.