I can't think of any way in Radiant or Quake 3 itself, but you could convert your map to .ase and load it into a 3D program of your choice. If you can't get .ase open, try the Online 3D converter and convert it to .obj or .fbx
You can use the q3map2.exe to convert your .bsp to .ase. To do so, creat a .bat file and paste the following text into it:
"[path to q3map2.exe]\q3map2.exe" -convert -format ase "[path to your Quake 3 map]\yourmap.bsp"
Run to .bat to start the process. If you have used patch meshes in your map, you have to compile with -patchmeta in the BSP phase, otherwise the patches will be missing from the converted mesh. The resulting mesh does work and is accurate, but the topology is probably messy due to the magic that happens in the BSP phase.