Without knowing a lot of information I can't make a 100% guarantee. However, you're 1.8Ghz K7 is almost certainly an AthlonXP 2200+.
Here is the difference between the Sempron 2200+ and the Athlon XP 2200+:
Sempron 2200+ (the one you want to buy): 1.5Ghz, 333mhz FSB, 256KB L2 Cache
AthlonXP 2200+ (the one you currently have): 1.8Ghz, 266mhz FSB, 256KB L2 Cache
As you can see the major differences are the clock speed (the one you want to buy is actually SLOWER) and the FSB (which is faster on the one you want to buy). If you buy this new CPU you'd have to replace the RAM to get it to work on a 333mhz FSB (that's IF your motherboard even supports a 333mhz FSB). And even if it does, you clock speed would go down to 1.5Ghz.
So my suggestion is to LEAVE your current processor in there. You will not see a performance gain by buying this processor.
Not necessarily... as I said in my post above, the Sempron operates on a 333mhz FSB while the AthlonXP operates on a 266mhz FSB. Certainly it can be underclocked to 266mhz, but what the hell would be the point???
Also, there's the issue of the BIOS recognizing a Sempron- something it was never designed to do.