Is it safe for me format my cloned internal boot drive?

You can do what you want. To be safe, do it in stages this way so you can verify it's all working.

1. With power disconnected from your machine, open it and disconnect the SATA data cables (the thin 7-conductor ones) from both drives. Now take the one that was on your old drive, and plug it into the new larger one. Do not connect a data cable to the old drive. Close up, turn on, and go immediately into BIOS Setup.There you should see your one new HDD and not the old one. Go to the screen where you set the Boot Priority, and make sure that this HDD is the one you are booting from. Save and Exit, and the machine should boot up normally with one large C: drive of about 930 GB total capacity.
2. Check the whole thing out for a day or two or more. Make sure you are happy that everything you need is there - in other words, the clone copy is complete and working perfectly.
3. Now shut down and disconnect. Go Inside and reconnect the old HDD to the second SATA port (the one you originally had connected to the new HDD.) By doing this, you have interchanged which drive is connected to which SATA port. Close up, power up, and again go immediately into BIOS Setup. You should see both drives detected. Go to the Boor Priority Sequence screen and make sure the new larger drive is still the boot drive, and the old smaller drive is NOT any part of the possible boot sequence. Save and Exit, and it should boot normally again. Now you will see the smaller drive as D: with all its old contents.
4. I assume at this point you do not need to preserve anything on the old drive (D: ) because it's all on the new drive anyway. So use Windows' built-in tool Disk Management to examine the drives in its lower right pane. Make SURE you are operating on the older smaller drive. First, Right-click on the Partition on that drive, and choose to Delete it. If there is more than one Partition, delete them all. Once it is all Unallocated Space, right-click again on it and choose to Create a Primary Partition, but it does NOT need to be bootable since you're only going to use it for data. You should ensure the size is the entire disk space. If the choices are showing now, also set up the Format options - use the NTFS File System and let it do the Full format, which will take MANY hours, so just find something else to do while it works. When it's all done, back out of Disk Management and reboot. Your system will have the large C: drive to boot from containing all your old stuff still, and an empty D: drive ready for data.