The simple answer is no.
The complex answer is maybe.
There aren't as many standards for laptops as for desktops so a lot of parts in retail laptops are custom made. There are "barebones" laptops available that you can add your own CPU, RAM and drives to. But assembling a laptop from scratch is not possible with off the shelf parts. If you were looking to save money, well, you can save a few hundred bucks off a high end spec in the $2000 plus range, but in the sub $1000 range, you'll be hard pressed to match the price of a pre-built one.
If you're gifted at metalwork, electronics and problem solving, you can make yourself a laptop style portable desktop out of mini-ITX desktop parts, but there would be a lot of handiwork involved.
In a very few cases, it's possible to get a deal on a popular model, from Dell or someone, that was a low end unit but that had expansion potential. For instance you might get a "glitchy" one or one with a bad power socket from eBay for a hundred or two, fix it, upgrade the base P4M 1.8 to a 3.4 or something, drop in a GB or so of RAM and a big fast HDD and for about $700 you'll have something that is about equivalent to a $1000 model, but without knowing the capabilities of each model inside out, you're liable to make a few hundred dollars worth of mistakes on the way, and end up "upside down" on the deal.