There were older Mac models where it might be possible to do that. Newer models may require a functional battery, even if connected to external power.
I myself had a model where I suspected that the battery died and it wouldn't power on - even with the battery disconnected (mine is that last version that Apple sold where DIY access to the interior is encouraged) with the power adapter connected. It did power again (I suspect the battery was intermittently failing) but since I got the battery replaced at an Apple Store it's working great.
I believe your model is one where Apple doesn't specifically replace the battery and return it to the customer with everything intact other than the battery. The battery is glued into the top case/keyboard, and a battery replacement service would involve replacing the entire top case/keyboard/battery assembly. In order to get it at a battery replacement price, the case and keyboard have to be in good working condition, although I believe routine wear on the keys is fine as those can be replaced. Those will go back to be refurbished with a new battery, and then will be made available as replacement top cases for both battery replacement service and top case/keyboard damage. The cost of the top case service is going to be more expensive since they typically won't reuse the part if it's damaged too heavily.