Yes, but how can you be sure rescuing you be worthwhile for the time machine's owner? It seems you are assuming time travel would be a low cost/low energy activity. What if the economics of time travel makes your rescue cost prohibitive?

From the question as posed it sounds like you were sent back in time accidently. It's easy to have an accident in the lab, I do it all the time. The question is, what will it cost to fix the damage (or retreive the traveller)? Worst case scenerio is they decide the best way to avoid damage to the known timeline is to kill you before you can mess anything up.

Imagine you are sitting in your cave when suddenly a small device pops into existence. It has note saying to hold it close to your body and press the red button.

Next thing you know, St. Peter is staring at you with a shocked look and says, "Wow, are you early!".

-Blast