Can I delete the 'EFI System Partition' without harming other data on the drive?

I am assuming that you originally formatted these drives on an Intel Mac (OS X) system.

Rather than paraphrasing what I've heard in other places I'll simply quote from the Wikipedia article for EFI System partition.

On Apple–Intel architecture Macintosh computers, the EFI partition is initially blank and not used for booting.

However, the EFI partition is used as a staging area for firmware updates; specifically it places a firmware flash utility (EFI binary) and data file (FD – "Firmware Device") in the directory EFI/APPLE/FIRMWARE which is then run when rebooting the system in "flash firmware" mode.

If deleted, the system will still boot, and the boot manager will still allow users to choose whether to start a Boot Camp partition or the default Mac OS X, but firmware updates will fail.

As I believe has been pointed out in other answers, the EFI partition is not used by Windows 7 and is not created when using a system which does not use EFI. In other words, if you are not going to use these drives as anything other than data drives then, yes, you can delete the EFI partition.

I'm afraid I did not take the time to experiment and find out if deleting the EFI partition will resolve the problems you are having with Windows 7 "seeing" your NTFS partitions on the drive. But it seems like it would be worth trying.

If I recall correctly you will not be able to delete the EFI partition from the Windows Disk Management utility. One way you could delete the EFI partition(s) is by running DISKPART from a (elevated) Window's command prompt.

I do this by first selecting the partition I want to delete and then verifying that I've selected the correct partition. Below is an example with one of my drives.

After you are sure you have selected the partition you want to delete, the command
delete part override
should delete it.

(If you don't care about any of the data on the drive and just want to repartition it, you could also use the clean command. For more info about it, type HELP CLEAN in DISKPART.)

Hope this helps.

DISKPART> list disk
  Disk ###  Status         Size     Free     Dyn  Gpt
  --------  -------------  -------  -------  ---  ---
  Disk 0    Online           76 GB      0 B
  Disk 1    Online          372 GB    32 GB
  Disk 2    Online          465 GB      0 B
  Disk 3    Online          931 GB      0 B
  Disk 4    Online          149 GB   255 MB        *

DISKPART> select disk 4
Disk 4 is now the selected disk.

DISKPART> list part
  Partition ###  Type              Size     Offset
  -------------  ----------------  -------  -------
  Partition 1    System             200 MB    20 KB
  Partition 2    Unknown             37 GB   200 MB
  Partition 3    Unknown            111 GB    37 GB

DISKPART> select part 1
Partition 1 is now the selected partition.

DISKPART> detail part
Partition 1
Type    : c12a7328-f81f-11d2-ba4b-00a0c93ec93b
Hidden  : Yes
Required: No
Attrib  : 0000000000000000
Offset in Bytes: 20480

  Volume ###  Ltr  Label        Fs     Type        Size     Status     Info
  ----------  ---  -----------  -----  ----------  -------  ---------  --------
* Volume 15        EFI          FAT32  Partition    200 MB  Healthy    Hidden

I just had a similar problem and delete part or delete volume were actually crashing diskpart!

On another forum I found the command "clean" which cleans the currently selected disk.

> list disk
....
> select disk 1
> clean

and now the disk is VERY clean. It does not have an MBR or GPT. In my case I wanted to install Server 2008 (not R2) and so I had to remove the GPT from a disk which had previously run Windows 7

I faced a problem with my Iomega iConnect "seeing" one of the NTFS partitions on my external HDD.

I had to delete the EFI partition on the drive (it used to be my MBP internal drive before I replaced it) and then everything worked fine.

If you are having problems with Windows 7 reading the NTFS drive, this could be a possible solution.