I don't think it would be detrimental IFF your rad is in decent shape otherwise. If it's not in decent shape, it may not have enough life left in it to warrant cleaning. That said, my copper radiator benefited quite a bit from having the tanks off and getting rodded out.
It's my understanding that some radiator cleaners are oxalic acid which you might obtain from your friendly local drugstore. I suppose there are other acids that would do the job as well, vinegar comes to mind. But with all, you're gonna need a good flush afterward which in and of itself might to the most good, depending on your ratiator's internal situation.
You should try this: remove the block drain that's on the right side of the engine, approximately below exhaust port for cylinder 3. Do this while the engine is cold and you won't get hot water all over yourself (DAMHIK). If nothing comes out either a) your cooling system is dry (unlikely) or b) your block is sludged up and this suggests the entire cooling system may be similar. Unfortunately without taking off the cylinder head, a gunky block isn't likely to be cleaned up using any short term chemical mix.