Hi - I did a quick test and found that hidden cells are overlaid using a paste command. In the test, I had an "A" in column A-E and hid columns C and D. I then selected a new TAB and placed a "1" in columns A-E and pasted this over the original spreadsheet with the hidden cells. All "1"s were present, so just like Auto-Filtering you must be careful there.

Unless there's a special version of the paste command that can handle hidden cells, the only sure techique is to copy individual columns and carefully paste them to the applicable non-hidden areas.