Complex Vector Art - Printing

You may want to see if your printer can provide a printed sample prior to going to full production, unless this is a one off design?

Can you increase the size of the brush to make a new brush and then reapply it? If you can increase it so that the dots are further apart, that should help the printer not worry about them filling in or disappearing.

I would second Monica's suggestion to expand the brush into editable paths. But going a bit farther, if all the objects in the texture merely contain an identical flat color fill I would release the compound path wherever possible.

Some printers will have a limit on how many anchor points can be in a single compound path object. We used to have an office printer that would reject objects that had over 5000 anchor points. The rest of the document would print, but the object going over the limit would be rejected entirely or only part of the object would print. Releasing the compound path is one solution to that. All those dots would be a whole bunch of individual objects with far fewer anchor points each. Another solution is using a setting to simulate compound paths when exporting to formats like EPS. The compound paths will be automatically sliced into non-compound objects.

"We have handled files with complex art like that before and it is unpredictable if problems will arise. We should be able to handle the art like that."

Standard we do not understand your question answer.  At what size are you planning to print the stipple pattern?  I can see a problem if you are planing to reduce the size of the artwork.  Try making the stippling about twice the size it is now.  That will increase the contrast and improve the appearance of the texture against the background.  You might also consider making the dots a little darker.  Get a ( printed ) proof before signing off on the project.

You can try and expand the brush.

Then run the pathfinder "Unite" on it, this might get rid of some anchor points.

Then also run the pathfinder "Crop" on it in order to "Expand" the clipping mask. This will get rid of hidden anchor points

What about the red shape? Is it part of the design? Then you could also delete the paths that are below it.