Depends on the service provider. VZW customers don't receive any special indication that the delivery failed or was blocked. The message will be sent as normal. However, depending on their VZW device, they won't see a delivery notification checkmark or "D" beside the sent message. I couldn't tell you what if any notice is displayed on phones from other service providers.
I tested this out on two different VZW devices on different accounts just to be certain: a pda phone (HTC Imagio) and a LG enV Touch.
If a number that is blocked tries to call the number, the caller hears the following:
"Welcome to Verizon Wireless. We're sorry, the number you have dialed has calling restrictions that prevented the completion of your call."
The free Call and Messaging Blocks on My Verizon expire after 90 days, while if you use the paid $4.99 Usage Controls service the blocks don't expire. You can block 20 numbers with Usage Controls as opposed to 5 on the free service.
I dont know if this person has Verizon, is there a way to find out?
You know you can block your number and call the person. See if the phone rings. If it does then you know your number is blocked.
You can look up the number HERE and see which cell provider the person has.