There's no such thing as a "Discoized" timeline. It's all the same timeline.
And yes, it makes sense. Pike literally assumed in the first episode of SNW that Spock would be his first officer if Una wasn't there, until he found out that La'an was there. Pike knows he's ready. Spock's also served on that ship longer than Gary Mitchell ever will, so it makes less sense that some lieutenant is going to come in and be first officer when a more knowledgeable and capable Spock is right there.
And yes, it makes sense. Pike literally assumed in the first episode of SNW that Spock would be his first officer if Una wasn't there, until he found out that La'an was there. Pike knows he's ready. Spock's also served on that ship longer than Gary Mitchell ever will, so it makes less sense that some lieutenant is going to come in and be first officer when a more knowledgeable and capable Spock is right there.