Sounds like a good idea to me. White radishes are supposed to be good to plant with squash, supposedly they repel squash borers. It never worked when I tried it but the squash grew well and so did the radishes. Cucumbers and squash are related.
Yes, I'd try it. For the reason Ridge mentions as well as for the food. The space for the cukes won't be needed right away and the radishes will be ready for harvest by the time the cukes spread there. 'Sides, radish tops will grow above the cuke vines.
Psst, Moxies! I grow my cukes on small fencing pieces about 4 ft. high. They love to grow up. It makes finding 'em easier. It frees more ground space for other veggies. It keeps the cukes from curling as much. Win-win-win-win!