Yes, existing Google Adwords and LinkedIn ads campaigns will be displayed in the HubSpot Ads tool when the respective account is connected.
However, data will not be displayed or tracked for LinkedIn ad campaigns created outside of HubSpot. You'll see a n/a displayed in the conversions and customer data columns for these campaigns.
To start tracking an untracked campaign, navigate to the campaign in HubSpot and click Add content or edit campaign. Add a new ad to this campaign from within HubSpot and pause the untracked ad (note that if the campaign is completed, you will not be able to add content).