Usually, REST based services require any tool which will consume it. Say, you have a GET call which will give you weather report of the day. You will need at least a browser to consume it. If you have to get the weather report of some other day, you will have a POST call which takes a date as an input. That you can not really achieve w/o any tool like POSTMAN plugin in Chrome.
Also, you can consider writing your own code which will consume this service and generate output.
So, as per your question, you can certainly test any REST service without any automation tool. But, to test these service manually, you will need some tool which will help you consume it.
Automation tools are mainly utilized to reduce your manual efforts. So, to achieve automation, you first should be able to do it manually.
