Perhaps, but it might not cover trip cancellation or trip interruption, which is probably the coverage you're looking for right now.
Trip cancellation insurance will reimburse you for your nonrefundable, prepaid trip costs if your trip is cancelled for a covered reason. Each travel insurance package is different, and you'll need to read the list of covered reasons carefully before you buy your policy.
Hurricanes are definitely special cases when it comes to trip cancellation and trip delay coverage. On all but two of the policies I checked, you have to purchase the policy before the tropical storm receives an official name. Some policies will only cover you if your accommodations at your destination are rendered uninhabitable by the storm. However, "uninhabitable" doesn't mean the same thing as "inconvenient" or "uncomfortable." HTH Worldwide Trip Protector's policy certificate defines "uninhabitable" as "the dwelling is not suitable for human occupancy in accordance with local public safety guidelines."
Reading the fine print is the best way to determine whether a travel insurance policy provides the coverage you want. You'll find yourself wading through lists of covered reasons that vary from policy to policy. For example, American Express Global Travel Shield Classic covers losses resulting from mandatory evacuation, but only if the evacuation happens during the first half of your trip. AIG Travel Guard Essential Basic doesn't cover mandatory evacuation, and only covers weather-related trip cancellation if there is a "complete cessation of common carrier services for 24 hours," which means that your airport has to close for an entire day for you to receive trip cancellation benefits. That's a tall order. iTravelInsured's Picture Perfect Vacation policy says it covers trip cancellation caused by a natural disaster, provided the disaster causes "complete cessation of services by a Travel Supplier for at least 24 consecutive hours" – another tall order, especially since the policy certificate doesn't define the term "natural disaster."
Your best bet is to buy travel insurance as soon as you make a financial commitment, such as a nonrefundable deposit, to your travel supplier. If you wait until a tropical storm forms, you've probably waited too long.