Does mining without a realistic chance of solving a block provide any benefit to the network?

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?

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