The quick answer is NO. (But see later.)
To use any hard drive over 137 GB (manufacturer's specs - Windows calls this 128 GB) you need a feature called "48-bit LBA Support" in three places. (And just plain "LBA Support", as it used to be phrased, is not enough). The Support needs to be in the HDD itself, and obviously WILL be there in a large drive like that. The Support needs to be in the HDD controller that the drive is attached to, because that controller needs to send drive addressing information using the full 48 binary bits required to access any position on a large HDD (The old original LBA system used only 28 binary bits, and that is why it can only address up to 128 GB of storage locations.) Thirdly, the Operating System also must use the full 48-bit address in its communications with the controller. We know that Windows 98 never had 48-bit LBA Support and never had it added in any Service Pack, so it will never be able to use large HDD's as you propose.
The unknown here, though, is the disk controller in your father's machine. Even if you upgraded his OS to Win XP SP3, it still might not work if the hardware in the machine is too old to have this feature. It became common in mobo controllers around year 2000, and it could be added to some earlier machines by updating the mobo BIOS with a newer version that had the feature added. So you'd have to do some info gathering to determine whether the hardware your dad has is able to deal with HDD's over 128 GB. And don't be misled by the older manuals that boasted of "LBA support for large hard drives" - in the mid-90's, "large" meant over 32 GB. (My older machine with Win 98 could not add 48-bit LBA Support via BIOS upgrade. When I moved its OS up to XP and added a large HDD, I used a 160 GB unit that was modified to limit itself to 137 GB so that it conformed to the hardware's limits.)
Here's a ray of hope if you want to pursue. IF you dad's machine does have 48-bit LBA support in its HDD controllers and BIOS, you MIGHT still get it to work under Win 98 (if he really wants to stay with that OS). The problem is simply that, in Win 98, you cannot deal with a "drive" over 128 GB. But one option would be to create on the 1 TB drive a series of Partitions, each no more than, say, 125 GB. (To do that, you would have to be doing both Primary and Extended Partitions, since you are allowed a max of 4 Primary Partitions on one HDD unit.) Each Partition on an HDD unit is treated by any OS as one "drive" with its own letter name. I have read posts here and on other forums that suggest you CAN use multiple Partitions under 128 GB with an older OS as long as the controller and drive both have 48-bit LBA Support. It's as if the controller and drive can keep the locations of all those Partitions clear, but the older OS never knows those details - it only deals with one "drive" at a time and always within its capabilities. If this interests you, look for more details around here and on Microsoft's websites and Knowledge Base. One thing to check closely - I don't have this answer - is HOW to create all those Partitions? In the Win 98 environment, Partition creation was done by a DOS utility called FDISK.EXE. I really don't now whether it could deal with a 1 TB HDD unit to create all those Partitions, considering that FDISK was NOT likely to have 48-bit LBA Support itself. The alternative would be to use a more modern OS like Win XP to create the Partitions and Format them on another machine, and then use that external device on your dad's machine and hope it can use those Partitions. You also should check whether Win 98 can use the NTFS File System, or whether you would have to Format each Partition as a FAT32 File System.
You might give this some thought, though (coming from a guy who held onto Win 98 on a Pentium 2 class machine for a long time). The processing power of that system is so limited that your dad may never actually use or store large files or large numbers of files. So, does he need / can he use 1000 GB? Will he ever exceed 125 GB anyway? That is, without actually changing to a much more powerful machine and application software and OS? Maybe a small external HDD is all he needs.
Oh, and another thing. Win 98 never had USB support built in. It WAS added late in its life (maybe only USB version 1.1, not 2.0, I'm not sure). So to use any USB external device, make sure your dad's machine has this feature added in.
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