If you bring your own car key into a Key Cutter, some will refuse, and some will happily offer the service but will offer no guarantees.
Many car key shells on Ebay etc are made of cheap material which is prone to breakages. The metal in these blades are often very hard which can damage the very expensive key cutting machinery.
Many of these keys are manufactured incorrectly in China and the dimensions are slightly off. This means they could seize or break in the ignition. With customers then blaming the person that cut the key instead of the sub standard product, it’s easy to see why many decline to offer this service.
If may be worth contacting the business before you bring your own key in to know for sure.
It is unlikely that a mobile auto locksmith will offer this service.