Can I dual-boot CyanogenMod 12 on 1st gen moto Gs? I have just found the CyanogenMod 12 and if I am not wrong it is modified android OS that has root access by default.

Can I just install it along with the system I have already and be asked what system I wanna boot like on a computer?
According to the Cyanogenmod site:

CyanogenMod is an enhanced open source firmware distribution for smartphones and tablet computers based on the Android mobile operating system. It offers features and options not found in the official firmware distributed by vendors of these devices.
CM is an alternative operating system intended to replace the one pre-installed on your smart phones and tablets. If you've got an older device that isn't getting updates anymore, or if your device seems unusually slow, or maybe you're sick of spyware, adware, and other unwanted garbage on your phone that you can't remove... Maybe your device is missing features or has been otherwise artificially limited in functionality. Perhaps you just could use a boost in performance... Or maybe you'd like to be more confident that your operating system has included some of the latest bug fixes...
If so, CM might be for you.

Essentially you are correct that it is a modified Android OS, with root access by default.
To install it alongside your current OS you would need to use a tool like Multirom which may not be officially supported for your device and can often be dangerous.
The Multirom thread even states:

It is dangerous. This whole thing is basically one giant hack - none of these systems are made with multibooting in mind. It is messing with boot sector and data partition. It is no longer messing with data partition or boot sector, but it is possible that something goes wrong and you will have to flash factory images again. Make backups. Always.