You can dry it and smoke it, the quality will be poor and it won't dry up to much weed but may as well give it a try. I didn't see any rot on it BTW.
That looks so much like damp off but it's happening on a mature branch and it's not down by the soil. Very odd, never seen anything like that before in 30 years of growing. Do you have high humidity problems? What strain is that? You may want to grow strains that are resistant to mold if you have high humidity and can't resolve that through ventilation or dehumidification.