Does mining without a realistic chance of solving a block provide any benefit to the network? Okay, before anyone votes to close this as a duplicate, I would like you to hear me out.

Since I began using Bitcoin, I always thought about miners as the people that effectively "host" the bitcoin network as if it were a website. I know this isn't entirely true, but its the analogy i've been using for a while.

What I want to know is if I mine Bitcoins on my mid 2011 iMac with the sole intention of helping the bitcoin network, will I be providing any real benefit to the network or will I just be fruitlessly trying to solve problems when the bigger, faster, mining-dedicated computers will ultimately beat me to it?

EDIT: Also, as an extension of my question above, could I be one of those miners that tweaks he software and only processes transactions with no fees to provide a greater benefit or would this approach still cause me to get out-hashed by bigger, better computers?
TL;DR:
Mining is heavy duty number crunching, your iMac is useless for that. Running a node helps the network and gives you your own copy of the blockchain. Your iMac should probably be able to do that.

Mining

The purpose of mining is to 1. achieve consensus about the state of the network, 2. confirm transactions, and 3. initially distribute the bitcoins. For mining your machine continuously shuffles the unconfirmed transaction pool and tries whether the current jumble resolves to a valid block. To contribute to the network, you have to have a chance at succeeding at finding a block. With a "mid 2011 iMac" you do not have a chance at succeeding at mining, as explained on In the ASIC-age, is it worth starting mining Bitcoin at home?. Its computational power for the purpose of mining doesn't register, it's a waste of money, time, and unnecessary wear for your hardware. To have any kind of effect, you need an ASIC today.

Running a node

The purpose of running a node is to 1. relay information in the network, 2. check the work of miners for validity, and 3. to have your own copy of the blockchain. Catching up with the network requires some computational effort, but nodes can be run on fairly lean systems. Personally, I run a node on a RaspberryPi 2B, it took roughly eighteen days to synchronize with the blockchain, but is now happily churning along. You can do that with your iMac, but really it's only useful if you either have it running a large part of the day (at least 6h), or are interested in having your own copy of the blockchain. Not sure how well an iMac deals with permanent load though, so maybe it's not the best machine for a 24/7 gig.