Nope. General Liability policies cover third-party claims against you - when you cause damage to someone else's property or injure someone else due to your negligence. It does not cover damage to your own equipment or personal property and it does not cover injuries to yourself or people working or volunteering for you.
Let's say you are putting on a Trade Show and need General Liability insurance to rent the conference center. They are requiring this policy to provide coverage in case you or your staff do any damage to their venue or if your negligence causes someone to get injured. But, it doesn't cover everything.
To put on a fantastic Trade Show, you've brought in a couple laptop computers to keep track of vendors and ticket sales. You purchased sound equipment and big screen TVs for a grand display. You didn't secure that big screen TV well enough and it came crashing down into all the sound equipment. While you were distracted, someone stole your laptops. It will cost you about $6,000 to replace it all.
Your general liability policy covers property damage, right? No, not in this case. Your policy only covers third-party property damage - when you or someone working for you causes damage to someone else's property. If you want to insure your equipment, you’ll need to look in to a Business Owner’s Policy or Property Insurance.