I'm not sure if this is "normal", but I wanted to share my own experience. One of my twins (now 4 months) did this at night for several months. Eventually, he was diagnosed with silent reflux (reflux without the spitting up) and put on medication (Nexium). I never asked our doctor about whether that particular behavior was related to reflux, but I did notice that it seemed to gradually get better both as he aged and after he got put on medication. He's still squirmy when we put him in bed (especially now that he's trying to role over), but he's much less noisy.
If your baby has other signs of reflux, it might be worth talking to your pediatrician, but I also agree that it's early on to be able to diagnose anything. In the meantime, we found that using loud white noise helped everyone sleep, because it made the grunts and fusses less disruptive while still allowing me to hear when he truly needed me.