All babies have they're own sleeping patterns - I say this, although i'm yet to figure our little one's pattern! Sometimes he/she is really active on an evening, right up until I go to sleep. Some days he/she goes for it all day! lol!
I've only been feeling strong movements for about 3-4 weeks so i've plenty of time to learn the pattern!
But yes, they can still move when you're asleep. My mum said I did nothing but keep her awake all night when she was in the last trim!
x