Yes, I would keep a NY chain and lock on the bike rack and carry with me the Ulock wherever I go. Not many thieves will want to steel a NY chain that is left behind unless they are willing to grind off the lock just for the chain. Leave the heavy lock behind and take the ulock with you just in case you need to do a stop and need to lock your bike along the way home.

Why a NY chain and Ulock? Because the only way to get through a ulock is either pry bar, jack, or grinder. Of the three tools, only the grinder is an efficient tool to break a NY chain with those mini lock that comes with it. So pretty much the thieve must use a grinder to steal your bike. Also he will have to cut twice because you have two locks. In this setup, forget the cable. The chain will replace that and beside, the same tool for cutting the chain can cut the cable but not so easily the other way around.