Can you appraise cards that are already graded?
In short: Yes. The grade and the certification number are part of the description, and the value still has to be researched and stated for your intended use.
A slab makes identification easier, but it does not make the value obvious. Two cards with the same grade can sell for different amounts depending on the grading company, the population and the market on the date in question.
I also look at the slab itself. If anything about the holder or the label raises a question, the report says so; see do you authenticate graded slabs?.
What to send
Photograph the slab front and back so the label and the certification number are readable. If you have several graded cards, list each one with its grade and certification number.
The purpose matters as much as the grade. A value for insurance and a value for an estate can differ, and the report states which one it gives; see which kind of value my report states. Photographs are kept with the report under the retention and consent policy.