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Yes, you can sit on counselling of two different states for BE and B.Tech admission. Preparing for an entrance exam like JEE Main or for that matter MHT CET or KEAM is no walk in the park. But, even if one crosses this hurdle with relative comfort, there are more down the lane that are almost like a web. Here we are talking about the complex admission processes weaved across different states. Take for example, the B.Tech admission process for other state candidates in Himachal, where you get 15% reservation for all India candidates; admission is first based on JEE Main rank, followed by merit in HPCET. Now if you move to Tamil Nadu, there is not much of a quota for all India candidates, but a limited 50 seats offered by Anna University, with admission based on 10+2 scores. Now, if you didn't know this subtle difference, you might spend fruitless time seeking admission to an institute in Tamil Nadu, based on your JEE Main score (if you had one), when you might have been better off applying for admission in Himachal. To ensure that no such thing happens and you maximize your chances, we urge you read up on the topic B.Tech admission for other state candidate. It will equip you with the correct and pertinent information, and make your life a lot easier.
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Thank you.

Hi Tejas,
This question is very subjective and the exact answer can only be given by the admission authority of that college. In general, there is a lot of criteria, which is considered for financial aid, your family economic conditions and capabilities. Your availability or sources of fund, your profile like (Entrance, GPA, Experience, extra-curricular, Awards and Recognition, etc.). If you are low in one area, you must have a strong hold over other areas. This may lead you to the admission but for the aid, it is hard to say because nobody knows the weightage they are assigning to your profile. One thing I can suggest you is that if you have a low GPA, you should focus on SAT experience (ask if your company can give you sponsorship) and your extra-curricular.