I encounter similar issue. You can check with Nest Group website which has some information about removing non-ionic detergent by HILIC. You can call and talk to Amos, the president, who is very knowledgeable on the subject and very friendly. I believe that it will work but not sure about the recovery (mass balance).
Here are some thoughts from one of our senior chemists...hope this helps.
This is probably something that will work to bind the Tween-80. However, it will require careful validation on the part of the user. First, many proteins come out of solution or aggregate when you remove the detergent. So mass balance could be an issue. Second, many proteins are not very soluble in the high concentrations of acetonitrile that would be used for HILIC binding of Tween. So mass balance could be an issue. Third, many proteins bind to the very hydrophilic, polar surface that is the fundamental feature of HILIC. So mass balance could be an issue. Even if the user is just doing a qualitative assay for identification, the potential exists for losing low abundance constituents of the sample.+
+For a great many protein samples, the reversed-phase desalting cartridge will be a more direct solution. Tween will bind more strongly to the cartridge than most proteins, and you can elute directly into the source. They will need to adjust the the gradient to allow some time for the protein to elute before the Tween is eluted and diverted to waste.+
+I would have a very different opinion if we were trying to measure the Tween.