Installation of a keyless entry only system (no alarm) will not cause any change in how the factory alarm operates.
You need to understand the following.
To set the factory alarm you open one of the doors and use the power door lock button to lock the doors. Or you could use the key FOB to lock the doors. When you shut the door, the factory alarm will be turned on.
If you just shut the doors and use the key FOB to lock the doors, the alarm won't be set.
To disarm the system, you can manually insert the key and turn in it in the proper direction which sends a ground signal to the CCM and the alarm is turned off.
If you want to disarm the system and use the key FOB, not only does the doors have to be unlocked, the keyless entry needs to send a negative going pulse to the CCM to simulate the manual opening of the door using the door key.
The VKE 1000 kit which was at one time sold by GM dealers seems to be a popular keyless entry kit.
Sells for around $60.00 by third party companies. It has relays built into the control box where some kits require external relays.
http://www.batee.com/corvette/keylessentry/index.shtml