Hi
I've been doing affiliate in dating niche with tumblr for a long time, its obviously possible. However, Tumblr loooovess to ban accounts, and if you're not careful you will fail pretty soon. However, if you protect your identity properly, it can be very lucrative source of traffic. At least nsfw traffic, I honestly don't know how it performs in other niches.
So, if you're going with tumblr, few advices:
1) better to have 10 accounts with 5K followers, than 1 with 50K
2) change your ip for every account (or every 2-3 accounts), either with proxies or VPN - I tried to automate with proxies and bot, still got banned. Than I switched to VPNs which is, in my experience, better solution, but the drawback is you have to do it manually.
3) change user agent for every account (there are some plugins for that)
4) use different email providers
5) don't spam too much - one link in caption is enough, don't go with clickthrough links to your offer; also, 40-50 pictures daily with link
6) shorten your link - change link shorteners periodically
I don't say that following the steps above won't get you banned from time to time, its just that it will minimize the possibility that tumblr connects all your accounts and terminate them all. By constantly developing new blogs you can get yourself a step ahead of their banning machine, and that can be pretty profitable.
God luck, here to help if you need advice.