yes you can register for account on adsense and if they think you have a good content they might agree but if you want quick and granted way register for one of adsense parteners like youtube
How many blogs does it takes from blogspot.com as your domain to be accepted by adsense registration?
I found this information please read and let me know your blogspot account have sufficient number of post (minimum 5+) then it’s easy to get your adsense account approved. If you have personal domain and host chances of adsense approval is very high.