production?? as in making and converting things? sure it would be able to but it would be slow, really slow.......
if you mean watching HD movies and what nots, what exactly is your mark? 1080p? 780? In theory it should since a dual core atom can do 780p no problem and that thing is much more powerful than it. What program are you using to watch the HD stuff, and is it like blu-ray or something?
well really it depends on your patience and what you do
if you can just set it and let it run overnight, who the hell needs a better proc? by morning it would be all done mostly and if you need more time go for a weekend/2 day render time.
if you do like massive photo shops with instant effects and what nots or adding post production things to videos in real time, then you need something like a i7 or at least a i5-750 or AMD Phenom II X4 940/955 (lowest imo you should be for "real time" or nearly real time stuff) with a ton of ram
and if you are doing encoding / trans coding, maybe a cuda or stream enabled video card from nvidia or ati is needed
again what exactly are you doing (apps and perhaps exact function of said app_, it's time constraints (how long can you wait, how patient are you, is it professionally done and your livelyhood depends on it) and how much are you willing to spend?
if you are talking like windows movie maker with crappy vid cams (like 320 res), it would have no issues even doing it in live or semi live fashion lol