Depends a lot on technique and personal stability. I would reckon to hold down to about 1/125th at 300mm on a monopod, slower if braced against a fence, rock or similar. Practise and see what YOU can hold it at and be happy with the results.
I cant stand monopods, for my subject (motorsports) i find if anything i get worse results as i have to pan in an arc, not straight lines. the best solution i have seen is a waist mounted monopod with a ballhead on the top. But this is used simply to take the weight of the lens, however the 100-300 F4 isnt really heavy enough to require support.