Short answer yes. We make it a point to add the processing fees to the client's invoice. Since we use Stripe its 2.9% + 30¢.

There's a bunch of different ways to invoice your client with a credit card option. The two we've used are our accounting software https://www.xero.com/and one time invoice with https://slimvoice.co/ (which as an additional $1 to the fees).