Is there any research/study/survey that looked at researchers' willingness to publicly share ideas that could potentially turn into a paper?
I don't think that somebody should expect people here on Acedemia.SE to perform literature search for them (regardless of their motivation for a question), hence the feedback you've received so far. Having said that, I have briefly looked at the topic and have selected the following references that might be of your interest. The caveats are as follows: 1) the references below are intended to be used mainly not as primary sources, but as containers of more relevant references; 2) scope of the studies referenced below ranges from some specific context to more general knowledge sharing;
Keyes, Jessica. Identifying the Barriers to Knowledge Sharing in Knowledge Intensive Organizations. ProQuest, 2008.
Wang, Sheng, and Raymond A. Noe. "To Share or Not to Share: Is That the Question?" Human Resource Management Review 20.2 (2010): 115-131.
Pilerot, Ola. "A practice theoretical exploration of information sharing and trust in a dispersed community of design scholars" Information Research 18.4 (2013): 18-4.
Wang, Sheng, and Raymond A. Noe. "Knowledge sharing: A review and directions for future research" Human Resource Management Review 20.2 (2010): 115-131.