Yes, you can use a welder with a generator. But remember to use a compatible generator,
by using an incompatible generator with your welder that can cause big problems and even be dangerous for you welding or may burn.
For example if you use a stick welder on a generator make sure you will need that generator which is compatible with each other.
If you want to go with the budget option, always prefer purchasing a welder generator with a built-in welding kit.