I am not well sure about it.... but i think it depends up on the domain to which the mail is send.
Sometimes it arrives instantly or with in a few minutes.Sometime it will be taking several hours.....
i dont think there will be an authoritative answer for this question.It all depends on many factors.Some times the mail may be queued for several hours in server, sometimes it doesn't.
I try it on hotmail and gmail and it is instantly i don't have yahoo mail so i can't test that...but if your server or x10 is online then you should get it instantly.. you get it if you set the codes right...
i have had many mail function tested in many servers.all the mails were delivered instantly. . GMAIL,yahoo,rediff,hotmail,in. . you dont need to worry about it unless you are not sure about the to address lol . .
quite often, email services, including yahoo, they tag the email as spam because it's mailed from php without proper headers, thus never making it to an inbox.
I had the same problem with when I signed up. So I think it is a problem with google appz email not with x10hosting email. Gmail, yahoo mail and most other emails can accept without problems.