It really depends, if they need a work to be done asap, being online may make them choose you, instead of others who are not online but is not the same every time.
As a client I have only ever cared about this once, when I needed an urgent task completed within an hour, and I sent invites to some online freelancers. But normally I don't send invites at all, because I get plenty of applications without them. So I'm probably not a typical client use case.
I think people usually prefer online freelancers so that they can talk with them on that time, In this way they can check thatis freelance suitable for thier job to hire. If we talk about our profile ranking I'm not sure but i think being online has not any effect on profile ranking. It do not increase any ranking .
A few months ago, I needed a small task to be done right away. Being able to see which freelancers were online helped me, as I was able to invite them and get an answer pretty soon afterwards.
Also, once I was contacted and asked to translate a letter right away. From those two experiences, I can guess that being online gets you invites, but mostly for small jobs.