07 tahoe remote start

By "remote takeover option" do you mean, pressing r/s button while engine is still running then you are able to remove key?

If this is what you mean, then no I am not aware of the ability of the factory starter to do so.  I work at a GM dealership and install a lot of r/s in the GM's with factory remote start. You can still use the factory starter but the aftermarket r/s offer much more options.

That is what I am talking about.

Do you know if the GM Advanced alarm module with the 2-way LCD remotes adds that option?

There is no factory option upgrade like that. Just go for a quality aftermarket 2-way remote start alarm. Most of  my customers usually complain about the lack of range from the factory transmitter.

Also you wil need to get a bypass module to interface with the starter and door locks on your truck