I've recently had to deploy software updates from Shavlik to SCCM for Google Chrome (v39) and would like to know if there is any way I could track the progress of the deployment? .i.e. since its deployment, how many machines has the software been installed on.
SCCM doesn't seem to have a lot built in for tracking the progress of a deployment - it just applies the updates when possible based on the rules you set up. However, you can go into Software Library > Software Updates > All Software Updates to see information about how many machines have applied each update. The fields for Required, Installed, and Percent Compliant should be useful.
If you need something more granular out of SCCM I'd suggest searching Microsoft forums/KB to see if there's any additional info on how to do that.