Got to take shipping into consideration.

Also places like eBay people who sell them use cheap power supplys and star wars looking cases and just wack in a good GPU and CPU and sell them at low prices. So you'd have to compete with there prices meaning you would have to probably to do the same.

I seen a custom building service once, this guy was charging 70GBP for the build service and then the buyer would either give him a budget and say what the computer was going to be used for and he would choose the parts or the buyer would choose the parts and give him the money to build it. But your going to need some kind of vouches and will have to be able to do some advanced stuff such as overclocking and custom loops if the buyer wants them doing.

Again take into consideration the shipping cost.

After shipping costs, the prices you would have to charge to be making money wouldn't be justifiably, unless you were making minimal profits, which in your case, wouldn't be worth it. In most cases, it's not worth it. If you can produce quality rigs, get good prices for shipping and make enough profit for labor costs, go ahead.

I'd probably be able to sell them locally so shipping wouldn't be an issue. So maybe it would be worth trying out

Depends if you were able to get enough attention. You might find it hard to find customers if you're only doing business locally. As long as you can make enough profit that you're happy with and aren't overcharging, go for it.