It'll probably meet the minimum requirements, but it will basically just be windows XP. With all of the stuff that MS "decoupled" from Longhorn in order to meet its deadlines, (that's a nice way of saying they are delaying most of the cool features of the OS, like Avalon, Indigo, WinFS, etc.), Longhorn will hardly be anything more than XP with a couple of reworkings, so it will probably work, but there won't be much of a point in upgrading that PC. You will need a 9800 Pro to at least to enable Avalon, and that card will run like crap with a 1.3GHz celeron. You'd be much better buying a budget socket 939 system for around $500 + $200 for longhorn, as opposed to $175 + $200 for the 9800 Pro and OS alone. $700 v. $375 doesn't seem like such a big difference when you're talking about getting a whole new PC. Try this - A64 3000+ - $140. Chaintech VNF4/Ultra - $90. 2x512MB Corsair Value RAM - $90 or 2x1GB Corsair Value RAM - $180. nVidia 6600GT - $160. $480 for a 1GB RAM system or $560 for a 2GB RAM system, both of which are 3+ times faster than your current PC, not even mentioning video, which is probably like 20 times faster, at least.
This is a good idea because
1) Longhorn is going to be primarily x64, with IA32 being kind of a legacy product. All new AMD chips and most Intel ones are x64 right now.
2) Longhorn's main new features (which will come a bit later) like Avalon, Indigo, and WinFS, will need a lot more CPU firepower than a 1.3GHz Celeron.
3) While the "Dual Core 4-6GHz" numbers were likely estimated back before Intel hit its wall with netburst, and assumed that we'd be hitting 10GHz here pretty shortly, dual core will be very important to longhorn, as it's task scheduler is being reworked to take advantage of DC chips. As such, moving to a platform that will let you grab dual core when it gets cheap enough (i.e. socket 939) makes a lot of sense.