Hi Barbara; Welcome to Growsonyou. My answer is no, the roots should not be removed. As epiphytes, the roots are an important part of the orchid's anatomy. If you like, take a look at my Orchid Blog to see how they grow naturally. Here is the link.

The Orchid Show at New York Botanical Garden
http://www.growsonyou.com/bathgate/blog/25917-orchid-show-at-new-york-botanical-garden

Agree with BG the aerial roots need to be left alone.

Thanks for your answer, much appreciated.

Barbara