Yes! The easiest way to hide the button for a product is to add a tag notify-it-hidden to the product using the Shopify admin.
If you're not sure how to add a tag to a product take a look at Add tags to products in the Shopify manual.
Using a custom tag
For some stores, the notify-it-hidden tag may not be suitable. For example, you may already have tagged products that won't be restocked with 'clearance' and would prefer to use that tag.
You can specify which tag will hide the widget button from your NotifyIt dashboard:
From your dashboard choose Customize, Product Page Button.
Choose the Behavior tab
Change the field Hide when tagged to the tag name you wish to use. You can only set one tag and tag names cannot contain comma (,) characters.
Hit Save button.
Hiding for a product variant
Shopify tags can be applied to a product but not to individual variants in a product so this method will hide widget for all variants on a product. It isn’t possible to use a tag to hide widget for selected variants.