No.
When you start tomcat, you will see the Tomcat process (ps -lef |grep -i tomcat)
----------------
java -classpath :/opt/apache-tomcat/bin/bo
otstrap.ja
r:/opt/apa
che-tomcat
/bin/commo
ns-logging
-api.jar -Dcatalina.base=/opt/apach
e-tomcat -Dcatalina.home=/opt/apach
e-tomcat -Djava.io.tmpdir=/opt/apac
he-tomcat/
temp org.apache.catalina.startu
p.Bootstra
p start
----------------
So Tomcat is platform independent because Tomcat is a java application.
There is NO 32bit or 64bit specific Tomcat for download from
http://tomcat.apache.org and the binary you download is working on both 32bit and 64bit.
I use CentOS 5.4 64bit with Java 1.5 64bit with Tomcat 5.5.26 for our company Java platform. There is no 64bit Tomcat binary available because there is no need for it.