Not really, let’s say the charity is for providing mosquito nets against malaria. The expectation is that any donation goes to providing more nets and not to pay for expenses and wages.
One receives money and then pays a 3rd party organization to install mosquito nets. This charity has very low "overhead" in that a huge portion of their income immediately leaves.
One receives money and then pays employees to manufacture and install mosquito nets. Even if this charity installs more nets it'll have higher overhead than the other charity since things like wages are considered overhead.
Second imagine two companies: - (a) One uses all the extra money on providing nets and delivering them to users in a low cost way so perhaps 0 overhead with the extra contribution. - One uses all the extra money to give it to pay staff, so perhaps 100 overhead for the extra contribution.
Both might be needed, but in general the reason overhead numbers exist is that people are more willing to give when their money goes directly to something they need.
See for example https://www.givewell.org/charities/top-charities
I think that givewell and charity navigator are valuable things. The charity that receives the bulk of my giving is considered highly efficient by both. But I do think that a narrow definition of efficiency does limit certain kinds of charitable organizations.
If you want 100% of the money to be spent on nets, just buy nets yourself, but that isn't enough to provide mosquito nets to the people in foreign countries who need them.
Although I partially agree with you, it is easy to show why your reasoning doesn't work. Let's say I create a charity to provide nets. I pay myself 99.99% of all donations and use the rest to fly somewhere myself and hand over 10 nets so I get a free vacation as well. And this is not a wholly theoretical discussion, I am sure there has been a charity like this.