If yes - how can I do this?
<aura:component implements="flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,force:hasRecordId" access="global">
Lightning App Builder and Page layouts are different concepts.
Lightning App Builder:
Short answer to your question:
Can I add a Lightning Component to Page Layout?
You can add the lightning component using app builder into record page,home page setting --> app builder --> select the page you want drag the lighting component from left panel to right side
For your requirement, you cannot directly place the lightning component in between the fields in page layout.
One workaround is , refer your lightning component in a visualforce page and add the vf page in the page layout.