Hello ,
Yes you can integrate with Google analytics via the genesys connector and then configure the utm tags in GA to pickup the data from enriched URLs.
Please find attached the document you can follow for the same .
Creating a new Web Analytics Account
Go to Administration > Platform
On the right hand side of the screen click 'new' as shown below
Steps
Select the Type to 'Web Analytics'
Select Partner to 'Other'
Then enter the Label
Then click Save

Setting up the Web Analytics Account
Go to Administration > Platform> External Account, click on Web Analytics as you can see below
Click Edit on the General Tab as you can see below
Then you will be asked to enter the domain(s) you will like to set up the tracking against, once you have entered, click Next.
Once you click Next, you will be presented with the Formula, now click the option to overload the function as shown below

In the same screen as above, you will see a text area below with the tracking code. This is place where you overload the script
with your Google tracking code.

As you can see in the above screen shot, the following code has been added:
&utm_source=NEOLANE&utm_medium=email&utm_campaign=<%= message.delivery.internalName %>
Note: message.delivery.internalName will get the internal name of the delivery and that will you're the value of utm_campaign
Setting up Web Analytics option on the delivery :
Now go to the delivery where you wish to set the tracking on.
Inside the delivery, click Properties and then go to Web analytics connector. From here you can choose the web analytic account
you would like to use for your delivery.

Regards,
Adhiyan