It is and (in my humble opinon) it's a good idea.
I've never liked the idea of learning servlet programming in an
IDE.
In order to have two copies of Tomcat running on the same machine, you need to change a couple port numbers. If everything in Netbeans is happy, don't disturb it.
Download the ".zip" version of Tomcat (assuming you're on a Windows machine) and unpack it. We'll call the directory it creates 'tomcat' (as apposed to apache-tomcat-5.5.blah blah..).
Open up tomcat/conf/server.xml and change the non-secure connector port from 8080 to something else like 8081.
Then, change the SHUTDOWN port from 8005 to something like 8006.
What you change them to is not really that important as long as nothing else is already using those ports.
Now, when you start up this version of Tomcat, you'll access it with:
http://localhost:8081