Hey, @Tastefulbliss. Great question!
No, you should not set your store address to be the same as your dropshipping vendor’s warehouse address. Your store address is specific to your business’ information, so you must set it to the address where you are located and running your online store from.
In general, your dropshipping supplier’s address won’t be added anywhere in your admin. For example, if you’re using an app like Oberlo to dropship with, then the vendor address should especially not be associated with the shipping address. This is because it's recommended not to use calculated rates when dropshipping. Take a look at the Help Doc on Shipping strategies for dropshipping for more information about how to set up the best type of shipping options for your business.