A heavy-duty gazebo can withstand strong winds of up to 34mph when adequately secured. While permanent gazebos may survive even higher speeds. You may wish to add an anchoring kit, rope and pegs or weights for extra security.
In short, yes. This way, you can avoid unnecessary accidents or prevent your gazebo from blowing away. Most structures come with anchoring kits. However, your gazebo's base will play an essential role in deciding how it should be secured.