Does resorcinol give positive iodoform test? It's given in my book that other than the usual compounds that answer iodoform test, resorcinol (benzene-1,3-diol) also gives positive iodoform test.

Is this because of tautomerization which gives a diketone with an active methylene group? But why should a ring lose its aromaticity by doing so?
There is an equilibrium between the keto enol forms, however small the keto form may be as a contributor. The rest is as you say. The precipitation of iodoform drives the equilibrium further to the products, as per Le Chatelier's principle.Of course, it is not in all cases where the equilibrium is controlled by such factors. The net gibbs energy change for the reaction must be negative.