To append to my previous statement, i now know you will be kicked, as you are violating the service agreement you have signed...
You can read it here
http://www.hostmonster.com/cgi/info/terms.html
to sum things up though,
What "Unlimited" DOES NOT mean. Hostmonster.com employs complex mechanisms to protect its Subscribers and systems from abuse. Hostmonster.com's offering of "unlimited" services is not intended to allow the actions of a single or few Subscribers to unfairly or adversely impact the experience of other Subscribers.
Hostmonster.com's service is a shared hosting service, which means that multiple Subscriber web sites are hosted from the same server and share server resources. Hostmonster.com's service is designed to meet the typical needs of small business and home business website Subscribers in the United States. It is NOT intended to support the sustained demand of large enterprises, internationally based businesses, or non-typical applications better suited to a dedicated server.
The key phrase...
or non-typical applications better suited to a dedicated server.
This is a very important note... RunUO is intended to be run on a dedicated server, it is not a web application, and thus, chances are you will violate the terms of service.
The other obstacle you will run in to is port issues, chances are they are only unblocking 80, 8080, 21, etc... normal FTP, HTTP ports, not 2593...
I get that dedicated hosting is expensive, and this is an attempt to alleviate some of the payment, but to me, the cost is valid. You will lose your host, there is no doubt in my mind about it.