Yes.
I had my Husqvarna Model 46A reamed from 9.3x57 to 9.3x62 last year. Works fine.
You need to seat your bullets slightly shorter than the listed maximum COL for 9.3x62, but not much. My loads are set to COL 3.229", instead of 3.29" that is spec for 9.3x62. Doesn't make a lick of difference (I checked with my gunsmith first, who has done lots of these conversions). My rifle was very accurate as a 9.3x57 and it is still very accurate as a 9.3x62, now it just pushes bullets a bit faster and it's easier to make brass (from commonly available 30-06 as opposed to less available 8x57 mauser)
BTW, don't overlook the plain, old 9.3x57 as it is. It can be reloaded to about 100 - 150 fps of the 9.3x62, and can generate energy levels of 3200+ ft/lbs. Many 9.3x57's have a long throat and you can actually seat your bullet far enough out that the COL is only about 0.15" shorter than a 9.3x62, making more room for more powder than your would expect in a fairly short case shooting a big bullet.