Does my Apple MacBook Pro have to have been previously connected to my wireless connection to connect it to that network to complete an internet recovery?
Short answer: no. Any Mac that supports Internet recovery could theoretically boot to Internet recovery even with the hard drive removed. Press and hold command-option-R immediately after powering on the mac. If it does not detect a physical network Internet connection, it will prompt you with a drop-down menu displaying a list of available wifi networks. Once joined, it will take a REALLY long time to boot, but eventually it will load a recovery OS. Here you can reformat your hard drive (or find out if one is installed), reset your password, access Safari and, of course, reinstall your OS.
I had this problem myself not too long ago. From what I read online error 3001F means that your Mac is having trouble talking to Apple's servers. The common suggestions being that the router is doing something unexpected or the signal strength isn't good enough.
The way I solved it was connecting through another device; using the hotspot facility on my phone instead of trying to connect to my router. The download does take a long time but it did succeed on the first attempt.
Hope this helps.
No. It should automatically connect, but in the case that it doesn't, it will offer you a list of wifi networks that you can connect to. Pick the one that you have access to, and it will connect. After that, it will start downloading the recovery image, and you will be able to reinstall Mac OS X. For more information, refer to http://support.apple.com/kb/ht4718
I am wondering if it is possible to connect directly to the router with an ethernet cable. That will give you better connectivity and faster throughput...
The non-retina (current) model has a built in ethernet port, so all you would need is an ethernet cable. the current) retina version would need the thunderbolt to ethernet adapter but should still work fine in recovery mode.
Failing that, if you have a local Apple store, try using their WiFi.
I've been facing this problem right now. For some reason, the MacBook wasn't showing the Internet Recovery Wifi menu and was not connecting. I was able to choose my connection booting using the Apple Boot menu (holding option key).