Can This Harm Currency?

I believe this is a form of 'pressing' (to get the wrinkles out) or otherwise doctoring a note, to make it appear higher-grade than it actually is. Both are generally frowned upon.

It's the same as ironing them, using heat to straighten folds. No matter how fast you do it the embossing and intagio will get flattened.

Depends on what you are trying to accomplish. Ironing a note will get out wrinkles if done properly. If the note is high grade, embossing will go away. So TPGs designate "great embossing" which pretty much indicates the note had not been pressed in the past. Lower grade notes with many wrinkles may benefit from being pressed. I would not use a curling iron to press them though -- plus it might embed some unwanted hair strands.

Washing/ wetting and ironing bills won't harm them per se, though they may lighten up the ink a bit depending on how much it gets worked over. For practical purposes of a regular bill- no harm. For a collection, it will harm the value. It does change the feel of the bill which is now crispy but apart from the crispy feeling of a real new bill.