They certainly could! That's a basic part of the deal when you offer something as open source.
I wouldn't choose to aid such a project, UNLESS I felt that JetBrains (the company that produces IntelliJ) was being harmful to the community of users.
A perfect example would be OpenOffice. While it was well-run under Sun I thought most effort should go to a single project not to works. Once it turned evil (Oracle) I thought all support should go to LibreOffice.
