Can I integrate Surfly through a Tag Manager?

Yes, you can. But tag managers do come with certain limitations.

If your users have an ad blocker installed, you run the risk that it will block the tag manager too. This is a side effect of ad blockers, as many of them block the loading of scripts from third parties. This means that these ad blockers would block all Javascript loaded through the tag manager, not just Surfly's. 

Therefore, it is advisable to add any code snippet to the website directly.