Can I check if a message has been sent successfully using Radiohead_ASK?
There is no concept of "did the packet arrive", only "did it get sent" - and by "sent" I mean the data squirted out of the data pin for the attached module to send.

These 433MHz modules are dumb. Very dumb. You toggle the transmitter's pin high and low and the receiver sees that toggling, if it is in range, and toggles its output pin to mirror the signal.

The only way you can know if the packet arrived is if the receiver also has a transmitter and the transmitter also has a receiver. When a message arrives at the receiving node it sends a message back to the transmitting node to say "I got it". That takes a lot of work to get right, though. Especially since the original message may have arrived fine, but the acknowledgement didn't, and all sorts of horrible things can happen if you don't handle packet sequencing right.

Better is to pick a better module that does all these things for you, such as the nRF24L01+ with Auto-ACK turned on.