To answer the question: most likely they will not. :(
Some people got pretty sad that Kara quit CatCo last night, mentioning how it's always been so important for Kara to be both a reporter and Supergirl (because she is both); even mentioning how Clark and Barry got to keep both aspects of their lives.
And it's true, that was pretty sad 😔
What's also pretty sad is how lost she feels, how overwhelmed, how she feels like she can't fully succeed at being neither a reporter nor the superhero that National City needs because National City needs both at the same time.
And that's okay.
It's okay to feel that way. It's okay to take your time to figure out what you need to do. It's okay to focus on one thing at a time - that by no means signify that something lost its importance to you or that you won't get back to it.
It's okay to wait to be ready to give 100% of yourself again.
Kara quit CatCo. Doesn't mean she quit it forever, or even quit being a reporter forever.
And she's aware of the toll that quitting something she loves so deeply will take on her, as well as the toll it'll take if she keeps both sides going right now.
"I'm not here fully. And there's too much at stake right now".
The Girl of Steel once more sacrificing her own happiness for the sake of others.
We know our Kryptonian baby has more than enough strength and perseverance to go back to having both parts of who she is when she's ready again.
Now, since this is the CW we're talking about *🤦🏻♀️ fml* the concern is... will they show that? 😔