Yes, google adsense approves a blogspot.com blog. You can open your account on adsense and add your blog to it. You will need to wait for 48 hours for approval. But before applying on AdSense, you need to make sure that your blog is compatible with AdSense.
I recommend that you should apply for adsense only after you blog is 6 months old. And your blog should have at least 20 new posts. Post should not be copied And there are some pages on your blog such as About me, Privacy Policy, Terms of Use and Custom 404 Error Pages.
Hope this helps.