Does Mark paid in vendor payouts send the money to the vendor?

No. WCart doesn't transfer money to vendors. In Vendors → Payouts, Initiate payout groups the vendor's unpaid earnings into one payout with status Processing.

Send the money yourself, for example by bank transfer to the details in the vendor's Business & Bank section. Then click Mark paid so the payout shows as Paid. You can see what each vendor has earned under Vendor Earnings.