While certainly not ideal, I did use a 416 Taylor (Mauser M98 rifle loaded with 410 grain Woodleigh bullets and 2350 fps muzzle velocity) for plains game in Tanzania. I brought it as a "one rifle for all" primarily for Cape buffalo hunt use, but served its purpose on Thomson gazelle, Olive baboon, Black-backed jackal and a Kirk's dik dik. The latter being quite ironic, as this was the smallest African animal I've shot with the largest caliber rifle I own, which also was used on the largest animal, a Cape buffalo in South Africa.
If you plan on bringing the 416, use solids on the small to medium sized plains game. The above referenced animals were shot with the solids which penetrated easily but did not do extensive damage. The furthest shot on the gazelle, was about 220 yards. With a bench rest, the rifle shoots at approximately 1" MOA accuracy which conceivably, I could push shots out to 300 yards to take plains game. Off sticks though and a 7 power scope, however, I'd limit shots to about 200 yards in the future.
So while my recommendation is yes, you could, realistically the shots would be closer (to 200 yards maximum) and suggest you also bring solids. The 416 would provide some good "smack down" capability on eland or zebra using soft points. Standard Cup and core bullets are good as the "softs" and there are many good manufacturers of these bullets, including the Swift A frames referenced in the previous post. I use 0.416" Rigby 410 grain Weldcore RN SN Woodleigh bullets as my "softs." I would recommend against mono-metal or gliding metal bullets at relatively greater ranges (such as Barnes TSX, all copper types, etc.) as they would not likely have the velocity to properly expand and act as "solids" anyway.