It depends what that "invisible software" of yours does with the
data that leaves your computer. If it encrypts it, sent to a
third-party server which decrypts the data and then send it to the
destination, I would say you're pretty much safe from any form of
tracking by your ISP. Anything less, and your ISP can dig out any
data that leaves the modem at your house if they wanted to.
You may want to consider VPN services such as Relakks, provided by
a company located in Sweden,
if true anonymity is essential to you.