Yes, resorcinol gives iodoform test.
This is due to the fact that a keto- form of resorcinol exists (via tautomerism as suggested by the original poster), which contains an active methylene group in a cyclic compound, this being a positive condition for the iodoform test.
However, the reaction will be slower than expected and is only driven forward by Le Chatelier's principle which states that precipitation drives a reaction in the forward direction.
Any question in theoretical organic chemistry asking whether Resorcinol gives the Iodoform test will always specify the rate (eg. A question with the statement: Which of the following gives iodoform test instantly? has Resorcinol being a wrong answer).