Can we do this?
will it run?
Probably: Tomcat was likely installed from a tarball and therefore is entirely self-contained. You may have some startup scripts under /etc that you'll need to move to get everything back the way it was, but Tomcat itself should be entirely under /opt/tomcat (assuming that's where it's been installed).
It seems to be a Java based product and it stands to reason that if the JDK is the same it would be fine.
That's a reasonable assumption.
I'm worried about any C code compiled for Solaris 9.
Unless you are using APR/tcnative, there are no native components to Tomcat. You may have some of your own, but you'll have to check that our yourself.
Why should we NOT do this ?
One reason: the opportunity to upgrade Tomcat during this process. IF you aren't on Tomcat 6.0.latest, you really should upgrade. If you are feeling confident, consider going all the way up to 7.0.latest.