In your example I would say mostly yes it does signal lower status, but you should do it anyway.

Willingness to collaborate is not as pure of a signal as say something like owning a winter home does to signal status because if I knew nothing about your willingness to collaborate I could still tell your status by examining your catalog of publications. Willingness to collaborate is an attempt to increase the lower status that you already have to a level that you would like to have. It's like attempting to win is signalling that you haven't won yet, but how do you win? You have to attempt to win.

I have recently been thinking about how incredibly useful networking is. I know successful people that have large and small social/professional networks, but if I examine only the people who I know that have large social/professional networks they are almost always employed and win more.