Sometimes a response takes more than two hours, especially on a weekend. Be patient.
In answer to your question, no. The TM backups are generated by a specific machine, and another will likely not see it as a valid source unless the machines are the same name. If you're looking to sync the two machines (or at least certain directories), there are far better methods including Automator. TM was really not designed for that at all.
Keep in mind that you should ensure the apps in question allow for multiple installations.