The only "strengthening" of the network happening during mining is when you solve a block. Mining without solving a block does nothing for the network. Leaving the client on, without mining, does help, but just mining and never solving a block is the same as never mining.
It most definitely is
not the same thing, if you have a small but non-zero chance of solving a block and many other people are doing the same thing. You can point to any member of this group and say "You're never going to solve a block, you're not doing anything for the network, so why even bother trying?", and you would be right most of the time. But some members of the group
will manage to solve blocks against the odds, and this
does help the network. Pooled mining actively encourages this behaviour by paying out based on the
probability of solving a block, however small that probability is. Most blocks are in fact solved by pools, not by solo miners, so there's clearly something to this strategy.