It will depend on the insurance carrier, and more importantly how long the leak has been going. This is sometimes difficult to determine, but if there are rotten boards, then it’s been awhile.
Most insurance policies cover “Sudden and Accidental Discharge of Water”, but most exclude “Repeated and Continuous Leaks”. The easiest way to understand this, is that insurance covers events (like Hurricane Matthew or a pipe break or tree falling) and not processes (like tree growing into the side of the house, rot caused by a missing section of shingles, or an undetected water leak).
All rental policies are NOT created equally. MetLife seems to have a more generous view of “unseen” damage, and will often cover claims that 95% of other companies would deny outright.
I am not affiliated with any specific insurance company, but I am an independent insurance adjuster and deal with the claims side for a living. However, I cannot give any insight into premium increases or renew ability issues.