Is there any evidence any Han immigrants to Taiwan were ever deported under the Qing?

Anyway, this is pretty irrelevant. It's just incorrect to say the population controls were effective.

The supposed population control did not last 200 years to begin with, contrary to the outlandish claims seen in this thread. Although the article mentiones "In 1759, for example, the gov't caught 25 smuggling operations in action resulting in the arrest of 990+ illegals." so it was enforced to some extent but ultimately immigration kept happening due to the natural demand.

Contradicting your claim the restrictions were effective.