It is indeed possible to have an account and start selling, even if you don't have your business legally registered.
Before going ahead, I would still recommend you check requirements with your local tax experts etc. just to make sure you're complying with everything there, but as far as Shopify goes, - it's as easy as going to this link here to learn more and set up your store.
What kind of products are you looking to sell? I would love to hear more about your business.
Lana | Social Care @ Shopify -Was my reply helpful? Click Like to let me know! - Was your question answered? Mark it as an Accepted Solution - To learn more visit the Shopify Help Center or the Shopify Blog