possible, not easy
Yes it would be possible to create a dual-boot system without the XP disc, but you would have to use someone else's dual boot package. There are paid-for versions like boot magic, and free versions like GAG booter.
You would attach your old drive either as primary or secondary drive into your existing PC. Then comes the hard part.
Your old Win98 setup will be very unlikely to boot. This is because the hardware it is now running on is very different to what it was installed on. It is perfectly possible to get it up and running, but it is an experts-only job.
I see no real reason why you would want to retain Win98 as an OS if you now have XP. Some reasons often given are for gaming, where the underlying DOS is a better platform than XP, or at least easier to get running games well. Most people, I feel, do not fully explore the many facilities XP offers to fool software it is not actually running on XP.
If your real concern is to access data on your old drive, then fine, just plug it in and you will see your old drive as a new drive letter, and can copy all you want onto the XP drive, re-format the old drive and use it for backup.