I'm Alex, with the Shopify team!
If you're intending to use Shopify Payments, yes - if you've set Shopify Payments as your payment provider, you can accept funds from your customers before completing the setup. This can be done for a limited time only, however; the funds won't be held indefinitely. After a period of seven days, your checkout will be disabled and any accepted payments will be refunded to your customers. For that reason, it's highly recommended that you finish setting up Shopify Payments before making any sales - just in case you encounter any delays completing your setup.
If you're planning on using a third party gateway, such as Stripe or 2Checkout, this won't be possible - you'll need to set your account up with that gateway before making sales through the Shopify checkout. If you're not using Shopify Payments but would like to start making sales right away, I'd suggest setting up PayPal in the interim, so that you can make sales while you're setting up with a payment gateway!
Hope that's helped! Please feel free to let me know, and you can always give us a call or start a live chat at any time. We're open 24/7 for your convenience and always happy to assist!
Alex | Shopify