No matter the table, you will be able to write or draw on top of it. However, depending on the texturizing it may be annoying to do so. For some of them, you may want to have a clipboard behind it to prevent jagged lines. In addition, some are designed with slats in the middle that will prevent you from properly writing.
But, in specific, with the camping tables that are designed with nylon fabric, you could get it tight enough so this would not be an issue. Now, as far as painting is concerned, the other aspect that needs to be considered is the excess paint being dripped on the surface.
A solution would be to simply cover the tabletop with several newspapers to accommodate for the extra paint. Basically, just treat it as a table you would treat in your home.