There's another way to do this. Assuming you've already exported the client, you can get the Limited Administrator to use the "Push Deployment Wizard" (foud in the Part_2 download from FileConnect) instead.
This version of the wizard doesn't create packages for you (which is why you'll need to have created ad exported a client installer first), but does the whole push install side of things. Being a separate tool too, it's is not affected by the permissions you assign to the Limited Administrator.
Just bear in mind, the target machines will still need to meet the general requirements for push install (admin rights, admin$ share access, remote registry service running, blahblahblah).
#EDIT#
Bit more info in the below articles:
http://www.symantec.com/docs/TECH183172
http://www.symantec.com/docs/HOWTO80805