Proper size is definitely important--it's not a good deal, no matter what the price, if it doesn't fit you.
In my experience, top tube length is the one that's most important to get right. There's a bit of latitude for adjusting the reach to the bars by changing stem length but this will change the handling dynamics so you don't really have more than a couple cm of adjustment. Adjusting the reach by moving your seat forward or back isn't really an option. The seat positioning should be largely determined in relation to the pedals. If the seat's not positioned properly with respect to the pedals, I feel like I'm constantly sliding forward or backward as I ride.
In your case--compare the FP2 geometry specs to your current bike, or take a ride on a bike with similar geometry. You can also try an online fit calculator, competitivecyclist.com for example, to give you an idea of what size you should be looking at.
In the end, there's no substitute for actually riding the bike in question, though some fit problems only become apparent after an hour or more on the bike.
Looking at the FP2 geometry, the top tube seems long-ish for the nominal size, and the sizing chart seems to run a little big. As an example, I'm 5'8" tall and generally prefer about a 54-55 cm top tube. Therefore, I'd probably be most comfortable on a 53 cm FP2 even though I'm 2" taller than the max recommended height on the sizing chart you linked. This is all, of course, specific to my preferred riding position and body geometry but suggests that the 55 cm frame might not be out of the question for a six-footer. Make sure you're comfortable on the bike (or one of similar geometry) before plunking down the cash, though.
Peter White Cycles has a pretty comprehensive article on bike fit that I learned a lot from--it's more qualitative in its approach but gives a good understanding of things to take into account.
In short--maybe, but it depends on your preferred riding position and body geometry.