**Yes. Definitely.**

There is a recurring theme in the show in which there are moments that show Sheldon *genuinely* cares about Leonard - all selfish reasons aside.

For example, in this clip towards the end, you can see one such moment:
[Sheldon talks to Penny when she is contemplating breaking up with Leonard.][1]

> **Sheldon**: Please don't hurt my friend.

> **Penny**: That is the last thing I want to do.

> **Sheldon**: Thank you. 

Even though Sheldon has a very high IQ, his EQ or emotional quotient is very much like a 10 year old's and he is shown to care for his friends and Leonard in a similar way (and with a similar reasoning) that a 10 year old child would.

  [1]: https://youtu.be/GLiqIucDqtA?t=2m54s