There is quite a thick line in my book between intruding and tagging along. With the latter, you tend to know at least one person in the group well, whilst the former has the addition of a 'special event' or occurrence.
You never knew who you meet. Two years ago, I felt bored with my usual crowd on the way to a party so headed in the opposite direction by myself, deciding to spontaneously knock at a friends house to see if anything was going on. My friends were actually having a quiet night in, but their housemate and one of her friends were heading off. So, I decided to 'tag' along and low and behold, one of them became my girlfriend.
A little bit of something different does you good.