Company Spying on my IMs at home?

I work at home and we needed to download yahoo IM in case we have any questions we want to ask supervisor while we work. We chose ourt own yahoo ID names. I use my own computer, but log onto company's remote desktop while I work. I know the compnay can probably view the IMs I write when I'm logged on to their remote computer. However, I am worried the company can also read my personal IM while I'm logged out of their system. Since they have my IM address I don't know if yahoo lets them view all of my conversations?