It could do, yes but highly unlikely. Do you have any idea what they might be achieving from this?
You say that you've contacted the company to get it removed so hopefully they should comply with this quickly. It would take Google a very long time to pick up on this anyhow. If the worst was to happen and you got penalised, you could just explain in Webmaster Tools and it would be fine plus you could sue them for a hefty sum as well. The chances of you getting penalised for this are next to nil anyway.
Can I suggest that you give them a call?
+48 914325555