SimilarWeb estimates that The Pirate Bay has roughly 315 million visits per month. On average, users spend five minutes on the site per "visit". While we have reason to believe that this underestimates the site's popularity, we'll use it as an illustration.

We spoke to Coinhive and they estimate that a user with a mid-range laptop would have a hashrate of 30 h/s.

In Pirate Bay's case this would translate to 30 hashes * 300 seconds * 315M visits = 2,835,000M hashes per month. If the miner is throttled at 30% this would drop to 850,000M hashes.

If Coinhive pays out 0.00015 XMR per million hashes, TPB would get 127.5 XMR per month, which is roughly $12,000 at the moment. Since the miner doesn't appear on all pages and because some may actively block it, this number will drop a bit further.

Keep in mind that this is just an illustration using several estimated variables which may vary greatly over time. Still, it gives a broad idea of the potential.