We are a multi-language Company with websites in different languages. Would it be possible to have the InviteBox system display a different language on each site from one account or would I need ...

You do not need more than one account for this purpose.You can set up different campaigns for each language within one account, there are no limitations.  Since you are inputting the words that will show up in each campaign, you can just input your message in the language you desire.