If the printer is relatively new ( 10 years or newer), this should not be a problem. Older laser printers that use fusing oil may cause some problems, but you don't see many of those anymore.
The digital paper that's made for laser printers is excellent. Digital = Laser. I've used gloss coated paper for offset presses in digital printers with mixed results. As long as it's for digital printers, you should be fine.
Please note that you will likely need to go to page setup in your print driver and select "glossy coated paper" as the source. This is because the user will need to run at a hotter temperature to fuse the toner to the paper. If it flakes off the sheet, it's not hot enough. If there's no select for glossy paper, select thick or card stock instead.
I run 100# gloss text and 80# gloss cover stock thru my digital laser printers all day long with perfect results!
It would not likely hurt your printer at all. The only thing that could happen would be if the toner flaked off and stuck to the fuser rollers, but running a few sheets of copy paper thru would clean it off.
Hope this helps!
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