Will I be able to move a 3D object/model and intersect with another 3D mode

I am very new to 3D world and to openGL. I am trying to understand if it is feasible for openGL to perform the below actions.

I might have many 3D objects in my page and allow users to move around as they wish but the movement should be sensible with proper 3 dimensions. Lets take an example of letter ‘T’, where I can have 2 separate rectangle 3D boxes and the users can move and form a letter T.

Finally, Is it possible to render this object and retrieve it back for the user as he modified.

FYI, I am preparing models or 3D objects using free software like Blender.

Please let me know if I need to share more info.

I have been exploring options but really want to get inputs before I start anything in detail.

Thanks in advance