This is possible. However it could be rather labor intensive if you did it manually. Since you need to do analysis based on the area of each poly before the merge, it would be beneficial to write a python script for the process. I will go over the manual workflow on how I would accomplish this below. If this seems to be too much or your data set is too big, please let me know and I can give you a hand with a python script / tool that will get this done for you.
Step 1:
Create a field within the feature class that will contain the "Area" calculation for each polygon after they are clipped.
I'm sure you know how to do this however just I linked below on how to create, modify and delete fields in ArcGIS Pro.
Fields view—Geodatabases | ArcGIS Desktop
Step2:
Use the clip tool to clip the polygons down based on a "Boundary" layer
This tool can be searched for in the Geoprocessing pane in ArcGIS Pro and I have also linked to the tool documentation.
Clip—Help | ArcGIS Desktop
Step 3:
Do an area calculation on the "Area" field that was created in step one VIA "Calculate Geometry" by right clicking the field name in the attributes table. You can also access the "Calculate Geometry Attributes" tool by searching for it in the Geoprocessing pane.
Step4:
Use the merge tool in the "Edit" ribbon within ArcGIS pro. Select the polygons that you want to merge and preserve the attributes from the polygon with the largest area. You physically have to choose which polygon to preserve the data from within the tool menu. FYI the Merge tool within the "Edit" ribbon in ArcGIS pro is not the same tool that can be found while searching for the merge tool in the Geoprocessing pane. The big difference is that the Merge within the "Edit" pane merges features while the Merge Geoprocessing tool merges datasets.
Let me know if you would like to explore a python script option.
Hope This Helps