Hank here from Shopify.
If you are not using Shopify Payments within your store, then no, you would not need to verify anything in relation to that. Are you using another payment method for your store, or just using PayPal?
The only key difference is that if you are not using Shopify Payments, then you would be charged a transaction fee (dependant on your plan) on each order as PayPal is a third-party payment gateway, as well as the credit card fee. Those charges are shown below and depend on the plan you are on.
You may need to verify things with PayPal as they are your payment gateway, but in terms of Shopify, the accounts team will only reach out if they need to verify something within your store, but not relating to payments, if they are not active.
Let me know if you have any additional questions!
All the best,