So, I admit that I haven't pushed 160 to 400, but I have pushed pro z to 3200 with EI 1600 and the results were fine. One example from a roll is (there was a url link here which no longer exists). N.b. the lighting was from a nasty mix of incandescents and candles and a distant street light in a little club (Spotted Cat, New Orleans) that was rather dark. I simply had no choice but to rate it higher and push. My assessment of the result was that the film handled it like a champ. The colours were okay (realistically warm, according to my memory), grain was okay, contrast was okay. I'd not expect any less from 160s... why not try it and report back to us. Chris, have you tried it? Any examples of mishaps from pushing 160s?
P.S. If I were to do this, I'd be tempted to rate the film for 400 and develop for 640 or even more. I'd probably not rate it at 400 and also push to 400, that'd likely give you some underdevelopment, I think. I rate pro h at 320 for normal development...