It depends upon the JEE Main and JEE Advance cut offs, If You manage to qualify the exam by achieving the cut off, You can apply for JOSAA Counselling. It should be noted that the EWS category cut off is lower than the General category cut off, so you can say yes, EWS category helps somehow
However It is usually advised to fill the choices as per the preference of colleges and departments, for example CSE in NIT Trichy is your priority followed by CSE in NIT Warangal, you can fill CSE at NIT Trichy at serial number 1 and CSE at NIT Warangal at serial number 2 and so on and so forth. However to get any NIT, you must have qualified JEE Mains and to get any IIT, you must have qualifies JEE Advanced

But the previous cut offs of colleges should be taken in consideration, it is better to research over the cut off of colleges then make a preference list of colleges and fill accordingly

For the college preferences and the courses provided by these colleges and to know which colleges participate in the JOSAA counselling, please go to the below mentioned link: https://engineering.careers360.com/articles/josaa-participating-institutes/amp

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Hello,

Definitely you should apply for the Counselling because you have a little chance of getting admission in some medium level of colleges and also you belong to EWS category. Now if you want to know your rank than you can use the below given link to check the rank and compare it with other colleges of your interest.

Thank you..