it is mostly about influence, but that is a multi-faceted concept. Influence can be a non-profit who has board members that could be key clients, or it could be a non-profit with a huge audience that they could share your name with for a referral.
More important in my mind though is the service that you can provide the client pro bono. Is it something that will show your best talents? The best part of pro bono work is you can pick the client since there is so much need out there.
A perfect opportunity combines both aspects. A well plugged in client that can give you exposure doing a service that you can do really really well is a great way to increase your visibility, get another portfolio piece, and help your community!
One aspect of doing something for free is that the results of what you did might not get proporly evaluated as the client might believe that you did a left-hand job. Getting them to pay at something, will have them give you a proper evaluation. On the other hand, I have given away solutions for free, which I knew were going to have a huge impact. The impact these solutions had, was so much larger than what I could ever sell them for. In this case I did not want to give the client the feeling that at least they paid for it, so I went to the other extreme. This lead so lots of sales leads and an open door from the same client.
It can also be a less stressful way to get some practice. I've heard of restaurants that will get free clients for a dinner (friends and relatives of staff or a local charity) just so they can test their kitchen and wait staff.
You can find flaws in your processes and build up confidence before moving on to paying clients.
In my opinion: no, it won't help you at all to offer your services for free. On the contrary. It certainly depends on your niche, but why would you ever give something away for free that you're good at? Especially if it's a professional service.
Don't devalue yourself. Whenever I see a free service, or hear someone offering me a specialized service for free, I turn away. Because if someone does that, that means they are unsuccessful and they NEED me. If they are unsuccessful, they can't be that good at what they do. Why would I ever want to hire someone who is not good at what they do?
Again: don't devalue yourself.