You can use pretty much any technology you like on the server side - even the humble CGI script. So yes, servlets will work. As most frameworks do, java has its own application server (which in the LAMP world is tomcat) which can be interfaced to a vanilla webserver: if the webserver is apache, the usual interfacing mechanism would be mod_jk.
Wether you'll be able to deploy it on the web development server, that very much depends on the platform; the accepted procedures, and your relationship with the sysadmins ;-). If it's a Linux/unix platform chances are in your favor, if not, inquire within.
Cheers