As everyone has already said, your equipment does make a difference, but no in the way I think that you may be thinking. It`s not so much about how much your equipment costs, rather if that is the right equipment for you. You can go out and buy an $800 top of the line free ride board that is super stiff and fast and it will make learning ride a misery for you. On the other hand, you could buy a cheapo Lamar that is a noodle designed for a beginner and really progress on it.
As a new rider, you want to stay really middle of the road cost wise. You don`t want a super cheap beginner board because you should out grow it`s ability to perform to your level fairly quickly. Look for an intermediate all mountain board and find a decent pair of bindings in the $150 range from Ride, Rome, Union etc and you will be in good shape.
I have a bit of a difference of opinion, considering my past riding history. I bought a 'budget friendly' beginner board 11 years ago. Rozzy Nomad 162w that is the equivalent of a Ford Ltd. A boat! lol. I'm curious why you mention that this new rider will outgrow his beginner board quickly. I went from barely making it down green runs to riding switch at times down double and triple black diamond runs on the same board. Not to argue with you, but I think a riders limit is in their head, not at their feet. I am speaking from a freeriding perspective. Unless someone hands me 1k to buy the 2012 Ride Highlife, I'll be sticking with my Rozzy when it comes to deep Pow days. Advanced technology would be the only reason for an upgrade if I had the money for strictly a pow board, but I've found that as long as I have the cojones, my beginner board still gets me down the chutes. Yes, others may have an easier time doing it, I'll admit that possibility exists, but I don't think that someone who has a beginner board is limited to beginning riding.
What I'm getting at is this. Please explain to me what I may be missing with regards to stunting abilities by using a beginner board?
I bought a 2011 Ride Machete yesterday, but the only reason for that was to progress with my riding into the avenue of freestyle riding. If I was JUST going to ride pow like I've done mostly, I wouldn't be getting a new board. Maybe I'll buy a new pow board and be like, wow man this is so much easier to turn or w/e, but it won't stop me from riding down the same lines as other guys with dope new setups. - Rider makes up 90% of ability or more. I've seen many dudes struggling to make it down blue runs only to discover that their bindings are so new they look polished, lol. If the board limits the rider, then wouldn't it be a good idea to outfit beginners with advanced boards with all the latest bells and whistles? Just some thoughts to ponder over. Don't want some kid thinking, wait man, I can't be an expert boarder because I don't have the new burton custom!