No. Adding UTM tags to tracking links will effectively break your link and mis-attribute your entries to the host under "Preview Promotion" which will hurt your average entry metric.
But, don't worry, DojoMojo's generated link will track the source, medium and campaign name for you.
You can put UTM tags in your welcome drip via your ESP to see how your emails are performing.
Only Hosts can track landing page traffic on Google Analytics.