It will not require admin priviledges if deployed via a GPO. While GPOs can be used for software deployment, before you push this on a production enterprise, you should create the package and link it to a "test" OU with a few users/computers.
If you have expereince with software deployment, you'll find that the GPO delivery method is not as robust as using a config manager product such as SCCM.
So if you proceed with deploying this via a GPO, you shouldnt use a batch file to launch the installation. GPOs natively support MSI files. If you want to be able to manage the life cycle, stay clear of batch files. With the MSI, the installation is self-healing where the computer can detect corrrupt files and other issues. In addition, if you need to remove the installation because the computer/user is moved out of the target scope, the GPO can remove the install base.
What I meant by package was a generic term used in software systems that deploy software. You should be able to do a search online for deploying MSI file via GPO. I am confident there are quite a few TechNet articles that will provide you with a step by step. Just try it out on a test OU first.
Glad to hear you were able to resolve this issue. If software management is something you are interested in and your environment is large enough to justify the cost, take a look at Microsoft's System Center Configuration Manager (SCCM). Its an enterprise system to manage your endpoints and includes software/hardware inventory, software distribution, remote control, and more.