Your authority to act as a corporation is solely a matter of state law and if you are incorporated as a nonprofit you can do whatever any other nonprofit corporation can do, except to the extent that you may have imposed certain limitations on yourself in your articles or certificate of incorporation as a 501(c)(3) charity.  Certain limits are required to obtain 501(c)(3) status, such as being organized and operated exclusively for charitable purposes and without private inurement. (See Ready Reference Page: “Articles of Incorporation Establish Basic Form of Nonprofit Corporations.”  Nonprofit Issues subscribers can read this page for free. Not a subscriber and want access to the article? It's a available in our store.) None of the required limits would affect your ability to obtain insurance. You can carry on business within those limitations without regard to your tax status. 

Federal tax status is a totally separate issue.  You probably ought to obtain your own exempt status, just for ease of operations and to avoid whatever costs or requirements may be imposed by the fiscal sponsor.  But the absence of separate exempt status will not change your ability to conduct business.