Does this compromise security?... I have installed many remote start systems with something similar to the product in the link. It is only activated when the remote start system is being used... It is hidden under the dash somewhere.
You could also cut off the actual key part if you wanted to... This would make it so even if a thief found the module, they couldn't use the key to start your car (doesn't mean they couldn't break the cylinder).
Is there some level on compromised security? Yes, but negligible.
What is the likelihood someone would know (other than the installer) -
1 - You have this type of remote start system that requires the extra key
2 - Where you live
3 - Where the module is hidden with the key in it.
Bottom line... If someone wants your car bad enough, they are gonna get it. Does this compromise the basic security? I think not...