Will iMessage be re-delivered when the recipient attains wifi access?

I went into Settings > Messages > Learn More and it says that iMessage only works in Wifi mode. I am on Wifi and I have been trying to send iMessages to another person. Each time I send it "delivered" appears under the message. The other person calls me saying that she has not been receiving my iMessages. However, when I turn off iMessage in Settings > Messages, she starts responding to me, implying that regular SMS messages work. I am wondering whether the iMessages that I've sent have disappeared forever or will she start downloading the undelivered iMessages them when she attains wifi access?