Yes,you can use Tumblr, Instagram and Pinterest to drive traffic to your blogs. But,it works best when your niche revolves around Comedy,Food or Fashion. With Tech,not so much.
You make multiple accounts and first try to build an audience. - It's tough to build a huge audience on a single account with limited time,so split your work by making multiple accounts for each niche.
To build followers,make a note of atleast 100 popular Instagram accounts/Tumblr blogs in the niche and start following them. Interact a little and also follow the FOLLOWERS of the popular Instagram accounts. Out of 10 people,atleast 5 will follow you back. Now just scale that up to multiple accounts and post content on your Instagram accounts,and then link them back to your blog.
Repeat this atleast for 2 weeks sincerely and you're gonna see amazing results.
You could also promote products(affiliate marketing) through these accounts. If you want to invest something initially,I would suggest BUYING SHOUTOUTS from large accounts. You'll get tons of traffic/followers to your accounts this way.
Good luck man.