We need to distribute Office 2013 to about 50 or so users and I was hoping MDT 2013 may be able to help me.
I have created a custom task sequence using MDT 2013 for installing Office 2013, I've just run litetouch.wsh and it will install as I want, provided that I am logged in as an administrator on the computer. Is it possible to set the task sequence to run with admin rights so that a normal user can run it so he/she can run the install from a shortcut?
MDT is not made for software rollout on already existing machines. Yes, you can manualy start the litetouch-script and run a task sequence - but this would be like every other installation of software: the process must run with administrative privileges. What you are looking for is for example SCCM, where you can rollout software on all machines in your envirement.
Without SCCM, you could use the software deployment mechanism in GPO, explained here. All you need is a MSI package, which should be no problem with Office.