In this case think of if as meaning 'so'. In the first part of the sentence the speaker is presenting the fact that he is planning to go to michiko-san's house and in the second part he's inviting Takeshi-kun to go along. In English it would be the same as:
I'm going to do X, so would you like to join me?
Like sova said, けど can be a queue to let the other person talk, but in the example above that is not the case. If the speaker had paused a couple of beats then Takeshi-kun would realize that he's being invited to come along without the speaker needing to finish his sentence
Then Takeshi-kun would need to either say yes or give an excuse as to why he can't go (culturally in Japanese you must give a valid excuse why you can't hang out with someone. Simply saying because I don't want to is rude so it's always good to have a response chambered.)
One bad habit that students of Japanese often have, is saying けど and then pausing to think. When speaking to a native speaker, they assume that person is either letting them talk or that they cannot express what they want to say. There are signifiers that you're thinking like あの but the differ depending on if you're talking to friends or teachers, etc. That's different subject so I wont discuss it further.
Sorry for deviating from your question a bit but I also wanted to clear up Sova's point and I don't have enough reputation yet to comment.