Itll work fine. I got FCPX running on a Mac Pro 2006
mBox is correct...MORE than fine!!! These new 13's are faster than two year's ago iMacs and MBPs...the 15s and 17s! They're incredible performers, and the Intel 4000 is a pretty beefy little chip for an integrated solution...definitely a usable solution for FCPx---and the way Apple has written the software to take advantage of BOTH the CPU and GPU.
Your statement about your cams you're using---the Canon DSLR (Go to canonusa.com and pull of the download/software section...there are plug-ins available for FCP that will speed up (by ten fold!!!) your ingestion from camera or card to your machine. That's one thing you'll want to augment FCPx with off the bat...the iPhone will ingest as well, very easily. You may want to transcode them to a similar format (ProRes)---but with FCPx that's not a necessity any longer (you can throw motion in practically ANY format on to the timeline and the program will do it's deal).
Even today's Airs will utilize FCPx efficiently. It's a well written piece of software, and done from the ground up for 64bit capability. As well, the two decent updates that have release have added a TON of additional benefits to the software itself.
Good Luck---and keep in mind, the MBP has a decent return policy and FCPx is now offered with a 30 day free trial---so you can try it out for a month and if you're not happy---return it for a 15".
...My background, motion is what I do for a living and have for 20 years. I use FCP7, FCPx, After Effects---Premier, and I've lately been playing with Avid (I hadn't touched it in 10 years!). I'm currently working on a 2009 MacPro, 2011 17" MacBook Pro (2.3/8gb RAM) and a pair or 2011 MacBook Airs. ALL machines have FCPx and the Creative Suite from Adobe. Even the Air runs FCPx well---it's the transcoding or finishing times you'll see slower progress with 'lesser' hardware. As a hobbyist though, Who Cares! Your editing will be just as fluent. When you go to finalize your project, take a break. Depending on the length of your film/project---we're literally talking seconds to minutes in real time saved. My 2011 MBP is almost as quick on rendering and transcoding as my Mac Pro. Just shows the technology evolution over the past couple years. These Ivy Bridge procs with intel 4000 are nice little machines for video.
Good Luck