If my phone has been down will my messages come through? (iphone 4)?

My mum has only just paid my bill and as it had not been paid for like 3 weeks they shut it off. Does this mean now its back on the messages i got whilst it was down won't come through?

if that is what it means is there any way of getting the messages i got whilst it was down?

You probably will not get all of your messages. At least in the USA, phone carriers only save undeliverable messages for a few days, not weeks and weeks. So it's very likely you will only get the messages that were sent to you in the last few days.

P.S. The exact amount of time before an unread message is lost depends on your phone company, not which type of phone you have. If you want to know the details, ask your phone company.