sure it can be done - that's where all our headaches begin!
lots of "challenges" - 90% unrelated to java [i'm assuming you want to write an installer in java?]
you need to know what "a local machine" looks like, or be prepared to write probes to find out ... OR have a kind enough owner of "a local machine" that s/he/they do(es)n't mind being left high 'n dry after a failed install.
some 'challenges'
1) target machine - OS
2) target machine - java version and env settings
3) tomcat - version and distro
4) mysql - version and distro
etc
the tomcat install alone comes in lots of flavors, depending upon the target environment. (last time i installed tomcat, i even had different env
string for RH versus other *nix... as an aside, have you tried jet? install is much cleaner last time i installed.)
all-n-all, your headaches will be more related to configuring a server than installing a java application, or even writing a java installer. unless all of your target machines are completely identical, then you will probably spend more time writing a *good* installer than you spent writing your app ... THEN will come the really fun part of keeping the installer up-to-date.
if you follow the approach of the 'big guys' in web apps, you'll put together your binaries, sources, and - if you're really nice - write an installation
doc and FAQ.
but good luck!