Even without the tagging, it still should not show as organic. Here's an article with more on tagging. In HubSpot, we've seen them fall under direct or sometimes Paid, without campaign allocation. Best practice is to get your UTM codes set up.
Note, whether or not the ads are run through standard Google Ads or Google Grants, the analytics/reporting aspect doesn't change.
Josh
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Josh Curcio HubSpot support and inbound marketing for OEMs, contract manufacturers, and industrial suppliers. HubSpot Diamond Partner & HubSpot Certified Trainer