I don't understand the comparison? Outlook and Thunderbird were pretty similar iirc. K9 does give me notifications when new email arrives. It's possible that it's every 15 minutes rather than instant: it hasn't been an issue for me so far. I know that Linphone is able to receive phone calls which is presumably by listening on a socket or getting activated by some inetd-type thing in Android. Maybe K9 could do similar.