This depends rather a lot on how you've written your software, and also on how your multiple servers would be configured.
If your system creates any (even temporary) files on your server, then you are likely to run into problems if your user moves from server A to server B during their session.
Likewise if you use session variables, you will have problems. Session variables are particular to a given server.
If you use a database, make sure that all your servers use the same database.
If you use any system commands, such as crontabs etc, you might run into trouble as well co-ordinating the execution of these across multiple servers.