I don't know about radish, but they will definitely eat turnips. I have seen them eat turnips on my place, but with a large enough plot, there were always enough for both of us. I would never expect to grow commercially without deer protection, however. My area is under heavy deer pressure though, and reports from hunters using turnip as food plots for deer are mixed. One thing, however, that deer seem to leave alone during winter is garlic/alliums.

There are some temporary fencing options for deer protection that these hunters use in order to get a stand started on their food plots, but the ultimate deer fence, IMHO, is at least seven feet, woven wire for the first 3 feet at least, then wires each 1 ft after that.

If you are selling, such a fence, with costs amortized over 10-20 years, is well worth the effort. One seller I know has been losing far more than the yearly cost he would have paid had he fenced. How disappointing is it to see your crops ruined? Then again, imagine what could happen if a herd of stray cows simply trampled across a garden ready for harvest! Fences are a must-do.

Here is a link that might be useful: Reports of deer food plots containing turnip