Howdy K P,
Not directly, though there are two other ways to access the Webmin API remotely, with XML-RPC probably being the most appropriate. It's pretty low-level, though. We're thinking on ways to improve the API situation, and trying to come up with ways to make high-level functionality of the rest of Webmin available as a library.
At this point, for something as simple as what you're doing, you might find using ssh is simpler. Just install keys for all of the "slave" servers that don't require a passphrase on the "master" server, and then run whatever commands you need to run. Something like:
ssh virtualmin@virtualmin.com '/home/virtualmin/bin/updaterepo.sh'
This is what I do to execute our software repository update script whenever I rsync my local repo to the virtualmin.com one. If you don't have to do anything complicated, like modifying configuration files, this might always be the simplest choice.
There's a quick guide to setting up public/private keys here:
http://www.ece.uci.edu/~chou/ssh-key.html