it is not a bad idea to use free webhosting with a free subdomain sites, but you ave to be very carfull for you adsense publisher ID you should know where to put it and where to not do. please check if the site is not agaonest adsense TOS, and it is ok but for my self, i prefer to buy a private domain name, and you will find hundreds of free webhosting providers that will accept you to add your domain. may bee 000webhost will help you doing that. i suggest for you to buy a .info domain from godaddy it is 3$ very cheap
Adsense is independent of domains or hosting. If you are talking about free hosting sites with free submdomains, then its OK I guess.