Yes you can. I do it all the time. I have the same problem as op and hardly ever buckle my boots at all. Still doesn't make the pain go away completely, but it helps. Well, maybe it depends what you mean by "great speed." I'm not saying i'm skiing 60 mph all the time, but, unless you're racing, who is?
to op: I've been looking for a solution to the problem for 4 or 5 years now and haven't found anything. No matter what a boot fitter does to my boots the pain doesn't go away. The thing that helps most for me is stretching. Has nothing to do with boot fitting, per se, but I have chronically tight achilles/calves/hamstrings and stretching every day does help the pain. Made it so I could at least ski pain free, for the most part, if i keep my boots unbuckled. Also using a golf ball to roll out the bottom of your foot after skiing will help loosen the muscles in there for the next day, so they hopefully won't cramp as quickly.
This is may or may not be the case for you, but if the cuff of your boot is especially tight around your calves it might help to have a bootfitter stretch them out a little so that more blood can get down to your foot.