If I understand you correctly - you have divided one drive into two partitions.
In order to use them, Windows needs to be able to find these partitions so it gives them drive letters.
The op sys is on the partition Windows boots up into is C:. If you've formatted it, the next partition is given the letter D: and other drives/partitions are also given a letter.
This is so Windows can find and list them.
If you remove the letter Windows Explorer won't 'see' it and the partition will become Hidden and not be displayed in Windows Explorer.
You will be able to see the drive/partition with no letter in Device Manager.
So really the answer to your question is: Yes you can remove the D: drive letter and No the partition will not just sit in drive (C:) as C: is a partition all by itself.
Think of partitions on one Harddrive as chapters in a book. Where the book is the Harddrive and the chapters are Partitions. Each chapter (partition) is separate to another but all are contained within the book (harddrive).