You would see a significant difference but not perhaps in things like word processing and the like but in gaming and any program that makes the sysytem work fairly hard. But I would like to point out a couple of things that in my opinion are poor in your choice, the hard drive you have chosen is quite low capacity in modern terms and for just a few pounds more you could get perhaps a 120 or even a 160 gig drive - worth considering. Also whatever drive you do buy make sure its the faster 7200 rpm drive with a 8mb cache as that will make some difference to the speed. The other thing is the choice of graphics card, I realise you say you just do a bit of gaming but with a FX5200 card if you try to play any of the new games it would just not be fast enough. You'd be better off spending a bit more and getting something like a ATI 9800. Also another thing is you make no mention of operating system. A friend of mine had an Emachines PC, in fact I think he still uses it but the OS, Win ME in his case was locked to the PC and cannot be used on any other PC. I wish to point this out as you may have to budget for a new operating system as well.
The trouble about upgrading is unless you can use a lot of the components you already have it can work out more expensive than buying a new system and in your case that may be the case, especially if you have to buy Windows XP as well. If I was you I'd have a good think about this as your PC may not be the best thing since sliced bread anymore but its by no means a dinosaur. If it does all you want at the moment then perhaps you should wait another 6 months or a year and then see whats on offer. I can't help feeling that after a fairly short period of time getting the new computer you have specified you may be a bit disappointed.