Yes and no. The IDE will run, but some functionality will be disabled.
The NetBeans IDE is a development tool and some of its modules depend on JDK libraries such as tools.jar and dt.jar that are available in full JDK installation only. When you try to run NetBeans on JRE, you will get a warning on startup saying that many modules have to be disabled. If you continue, the IDE will come up and you'll be able to work with it, but many standard features will be unavailable.
It is highly recommended to use NetBeans with a full JDK. The installer will even reject to install NetBeans when no JDK is found.
Source: NetBeans User FAQ