Can I block a customer from using it when generating a document?

It is not possible to hide a customer or disable it, but you can make use of the pop-up warning feature to add an annotation which will appear when you generate a document to that customer as a warning.

For this you have to access the client tab, go to the General tab > "Pop-up warning", make annotation and save.

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Once you generate a document on that client, such a pop-up notice will appear.