Yes. Short-Term and Annual policies can cover rented gear inside and outside of ShareGrid. They are not exclusive to one rental.
So if you decide that you need short-term insurance for an upcoming shoot but may have another project in the future, you can purchase a policy that covers that future project as well.
One thing to consider is that once you are doing more than one project a year, it may be more cost-effective to purchase an Annual insurance policy. This will cover you for a year and is far more cost-effective if you’re a frequent creator.