Combination of Disjointness and Gap Hamming Distance communication complexity
Yes, because (1) KLLRX prove $\Omega(n)$ information lower bound for Gap Hamming (for distribution over both YES and NO inputs), and (2) Theorem 3 in GJPW shows any such information lower bound holds also wrt distribution over NO inputs, and (3) BJKS paper shows that composing any function with m-bit OR increases the information complexity over NO inputs m-fold.