I agree with Velo Dog, in a standard weight magnum action rifle (around 9+ pounds) the 375 H&H delivers about twice the recoil of a 30-06. you will likely find it to be very manageable (as most do) and that rifle should prove fairly accurate. I wouldn't concern yourself too much with the barrel being fully floated. it shouldn't make a huge difference at the ranges you typically use this cartridge. of course if it really bothers you, it shouldn't cost much to have a gun smith perform a trigger job, action bedding, and float your barrel (normal work on inexpensive rifles). also keep in mind that CZ Safari rifles shoot pretty good and aren't free floated at all.
-matt
+1 with Matt85 on free floating probably not being worth fooling with on your new rifle.
Back in my ground squirrel shooting days, my experiences brought me to the conclusion that free floating rifle barrels made little to no difference on rifles with normal weight barrel contour and also, little to no difference for rifles chambered in rather low intensity cartridges.
Extreme light weight barrel contours, such as all these "ultra light mountain rifle" type designs, that are also chambered for high intensity cartridges like the 6.5-06, .270 Weatherby, 7 mm Remington magnum and similar, are the rifles most likely to benefit from free floating the barrel.
A standard weight barrel .375 H&H is very unlikely to benefit much, if at all from free floating it.
However, regarding resistance against cracking the stock in recoil, it might not hurt to have a Gunsmith glass bed around the action for strength.
Otherwise, as others have suggested, just shoot it before you start messing around with accuracy improvement modifications.
Very likely you will discover it already shoots well.
You can find comfort in the fact that a Mauser in .375 H&H is IMO, the best hunting rifle ever devised.
(And if Velo Dog said it in some computer forum, it must be true, guldangit).
Cheers,
El Doggerino, if you're not into the whole brevity thing.