Not automatically. Policies commonly exclude adventure activities, cold-water immersion, overnight camping, kayaking, mountaineering, skiing, or anything above a stated altitude. List every optional activity you're considering when you speak to the insurer, before you pay for the activity rather than after.
There's a second gate that people miss. Insurance cover does not guarantee the expedition team will let you take part. Participation is assessed separately against the operator's own safety, mobility, balance, endurance and emergency-exit standards for each activity. You can be fully insured for kayaking and still be told no on the day.
So there are two confirmations worth having before you book an optional programme: your insurer in writing that it's covered, and your operator in writing that you meet the participation standard.