Does clicking Sync now in Sales Channels send my new products to Google straight away?

No. For Google Shopping and Meta, Sync now only marks the feed as ready and updates the status on the card. Nothing is pushed. The feed itself is built fresh from your published products each time it is fetched, so new products are included automatically. Google or Meta picks them up on its own fetch schedule.

To get changes in sooner, start a fetch from the scheduled feed in Google Merchant Center or Meta Commerce Manager. Make sure the product is published. With Products to include set to Active only (the default, under Settings on the channel card), the feed lists only published products.