Yes, to an extent.
On the Nintex Form, set the Default value for each field you want copied to the new item to "Specify a value". Choose the Inline Function "GetQueryString" and make up a good descriptive name like "Title for the title field, etc. Repeat for each field - not sure it works on all fields types, but I have had good success. Write down all the names you came up with.
When you build the link for the button (non responsive forms only; just a regular link to responsive forms) in a Calculated Value control, you will have the URL to your new form (like htttps://mysite/listname/NewForm.aspx) and then add to it the URL parameter names and the Named Controls on the form that you would like the values to be. Be sure to select the Named Control and not Item Properties if you want the active value from the form.
You should end up with a base link that looks like this when you click on it:
https://mysite/listname/NewForm.aspx?Title=Title&Category=Category&Date=Date
Then you can create a target=_Blank, give the link a title., etc.
For instructions on creating a link within a calculated value control see this post:
https://community.nintex.com/t5/Nintex-for-SharePoint-Forum/How-to-generate-calculated-filed-value-into-hyperlink-in-Nintex/td-p/940