Off course it's possible. Sometimes, the domain doesn't really matter, all that matters is the contents and availability of the blog to be reached by intended visitors.
I have two blogs, one is a free blog with blogger and i've been able to make it popular by my efforts and hard work. I think I can call it a success because I have over a hundred thousands followers with hundreds of views on average a month.
The reason I have a second blog which is not a free service is due to probably some of the concerns you have. Sometimes a free service doesn't look official and can lead to missing some opportunities. Seriously minded businesses looking to do business with you might re-think their decision if they are presented with a free service blog since whatever venture they have in mind involves money. Nobody wants to do business with a partner who runs a free website.
Another problem with subdomains is that the address are kind of complicated and visitors are likely to forget the name or address. A domain on the other hand is quiet easy to remember as it involves just the name followed by an address suffix.
As a beginner, it's advisable you use free services like you have done to see how it all works out. If you get to a point when you believe you're getting successful as you wish, then you can put in the money and start using paid services.