I see from the point of contamination no real reason not to use the final bath with surfactant on the reels.
The surfactant is watersoluable, even remaining droplets would at the next run (developer) be diluted by several magnitudes.
But as the reel typically is used in a dried state, some argue that, after omitting rinsing the reel with plain water, out of the dried state a film of surfactant might built up and grow over runs. Finally hampering sliding new film into the reel. Others argue that such build-up actually is residue of gelatin, and thus the reels regularly have to be cleaned with hot water or with a strong alkali.
One may try oneself on a sheet of glass whether the used surfactant might build up if not rinsed off.
But there may be a approach where the surfactant is used in a seperate container nonetheless:
depending on type of reel used and ones manner of working, one may open the reel and let the film fall into a container with the final bath. Thus not out of an issue of possible contamination, but out of an issue of better handling of the film when taken it up for hanging.