I don't know specifically about the Tumblr app but I see this quite often on our wireless networks with other similar apps (Facebook, blogger, etc). I think the key to your answer is your companies attitude, rules, and how closely they monitor their web logs. 

Personally my view is if they allow personal mobile devices on their wireless networks then it's a risk they have decided to accept. Most companies will block whatever sites they don't want allowed anyway. So as long as you are maliciously trying to circumvent the web filter (for example using a anonymizing/proxy) then no harm no foul in my book. I think you have a legitimate excuse here. In my experience it's pretty easy to tell the difference in someone surfing the net and background application traffic.

It's technically possible they could trace it to you but I can't imagine it's worth their effort (again I don't know where you work or the culture).