The straightforward answer for Socotra is not simply yes or no: most governments currently advise against all travel to Yemen, and Socotra, despite being geographically distant from mainland conflict, falls under that same country-wide advisory for most travelers' home countries. The practical consequence matters more than any general risk warning - many standard travel insurance policies exclude cover entirely for destinations under a do-not-travel advisory, so a routine policy purchased without checking this may simply not respond if something goes wrong here.
Socotra is known for its dramatic Dracaena cinnabari, the dragon's blood trees that make the archipelago a UNESCO World Heritage site, and that draw is genuine. But access is the honest core of this page, not the scenery: reaching the island typically depends on limited charter or scheduled flights and shifting arrangements that can change with little notice given the wider security situation, and normal travel insurance assumptions about rebooking or evacuation do not reliably apply here the way they would elsewhere.
If you are traveling to Socotra despite the advisory, specialist high-risk travel cover exists for exactly this kind of trip, distinct from a standard leisure policy, and it is worth confirming with any provider, before you buy, whether Yemen and Socotra specifically are named as covered rather than excluded. A policy's silence on this point should be read as exclusion, not inclusion, given how consistently mainstream policies carve out advisory destinations.
Keep any documentation of your travel arrangements, local contacts, and communications with your insurer confirming cover before you depart, since a claim here will likely be scrutinized closely against the advisory status at the time of travel. Check current government travel advisories for Yemen immediately before finalizing any Socotra trip, since guidance can change, and never assume a policy provides cover for travel a government has advised against.