Can clients pay for appointments booked internally?

Yes. When you book an appointment internally, the confirmation email includes a link to view or modify the appointment. If the client follows this link, they will see "Would you like to pay now? Click here", which gives them an opportunity to pay for the appointment. You can add text to the confirmation email template (under Messages > Templates) suggesting they pay this way.

Also, if the client is registered, they can log in, view their upcoming appointments, and choose to pay from there.