The answer would be Yes. One of my friends had completed B.Tech in Instrumentation and Control Engineering from NIT Trichy. The course is definitely tough but the level of difficulty perceived may differ from person to person. And here is some of the information about the course.

Sheer multi-disciplinary nature of subjects :

• In the very same semester, the candidate will have to study a varied range of subjects such as Fluid mechanics, Material sciences and Circuit theory. 
• All of these subjects require a good knowledge about modeling in different areas of Physics as it is one of the most essential skills of an Instrument designer.

Involvement in Laboratory activities :

• Practical knowledge is very important. 
• Most of the lab exercises are worked in a team. 
• Thus to complete any task starting from designing, experiment and analysis within a particular given time is a bit of a challenge. 
• It is important for all the team members to work efficiently for the task to be completed.

Programming and Analytical skills : 

• It is important to have a good hold on C/C++ programming to understand subjects such as Data structures/Algo, Embedded systems, Control systems design.

Product design and Development :

• The candidate needs to come with new project ideas and develop it from scratch and make it an Industrial prototype. 
• This will require a lot of outdoor work, market surveys, meeting suppliers and customer feedback. 
• Teamwork is very important for such activities.

Design specification :

• Right from the lab exercises, most of the projects and products the candidate needs to work on have a clear Design Specification. 
• It is important to adhere to those specifications as it demands sincere and laborious efforts from the candidate which might be tough. 
• The faculty or project guide may also make things tougher.

These were some of the aspects that make Instrumentation and Control Engineering tough. The course is pretty involved and demanding. Though all these mentioned aspects and skills are required to be a successful Instrumentation engineer.

I have friends pursuing courses you mentioned above at either institute. Based on the discussion I have with them, here is what should be best for you,

1. The institutes can be considered quite equivalent to one another, but BITS Goa has an upper hand. 
2. M.Sc at BITS Goa can be specialized following the first year, during which you will be allocated a B.E course depending upon your CGPA. 
3. With a 6 CGPA, you can get Mechanical Engineering, which is quite an easy job. In contrast, it is better than ICE.
4. However, if your scores are high enough then you might get a seat in CSE. 
5. By the end of 5 years, you will be receiving a B.E and an M.Sc degree, which is nonetheless a smarter choice. 

However, the fees at BITS Goa are quite a lot. 

Admission to these branches is done through rank obtained in IPU entrance examination. However, instrumentation and control engineering is the least preferred branch in BVCOE.

Being a non-CS branch, the placement statistics of Instrumentation Engineering is not good. The level of difficulty of this branch is no less than CS or IT but then studying the course in a domain like Instrumentation Engineering and ending up being at Software Company doing the same as other IT/CS engineers are doing will not take you anywhere.

In the admission process, the basic order followed according to the branches is CSE, ECE, IT or EE, and ICE.

Below is briefly mentioned the perks and cons of pursuing Instrumentation Engineering from Bharati Vidyapeeth:

This depicts the information regarding instrumentation and control engineering in Bharati Vidyapeeth's College of Engineering, Delhi.