Should I Intern At A Startup Where There Is No Chance Of Getting Absorbed Or Focus On Getting A Job?

That's a wonderful opportunity . Grab it with both hands. Please ask yourself the following questions while working there to be assured that the ship is sailing in the right direction.

1. Do you enjoy the work?
2. Are you learning new things?
3. Are you able to make contacts and do networking with people who can help you land in a decent job?
4. Are you happy? Yes/No and why?

Work as an intern at a startup even after knowing that you will not be absorbed. It's so because you will acquire the right skills by working there.

Positives:

1. Find something hard, challenging and learn it.
2. It's not about what you do but how you do-Three workers were asked a question "What are you doing?" while they were laying brick during construction. First worker replied that he was laying brick, Second worker replied that he was making a room and the third worker replied that I am contributing in construction of a wonderful building. All were doing the same thing but their response was different. We all have to be like the third worker as seeing the bigger picture keeps us motivated. {From the book- You can Win}
3. Networking-You can make contacts with other like minded people by working at that company. It will help you in getting job offers from well established companies.
4. It will help you to land at a job at MNCs- Treat this as if you are working on a live project as an internship. It will boast your confidence, build your knowledge and would help you during on/off campus placement.  My sister is in INTEL because she worked hard on a live project learning many things at a healthcare startup. Only two people got selected in INTEL from her branch and both worked at the same startup.
5. Knowledge is Powerful- I can say so confidently as my sister told me that recruiters were impressed with the knowledge she accumulated during her internship at the startup. It provided her with a cutting edge advantage over others.
6. Industry Exposure- You get to know what you like or dislike much earlier than landing in a full time job. While working on Startup, you'll get hands on experience even when you are in college.
7. Don't limit yourself- Learn a bit about HR, Accounts, Marketing, Technical aspects, Getting Investors, etc. You never know, while working as an intern, someone might get interested to hire you at a MNC.
8. Lucky things happen when we keep doing many things.- We had an interactive session with the management and I was quite expressive in my feedback. Suddenly, our Project Manager said that we should start a magazine and I couldn't resist spilling the beans. I told about my study of human behaviour and then their curiosity lead me to reveal about my online activities like writing on Quora, running half a dozen blogs with over 500 blogposts, getting my suggestions featured in Business Insider, etc. I have been appreciated by HR, Project Manager, and many employees who were clueless about it. Most likely, I'm going to start a magazine for our Project after accessing the viability. That's a big thing for me and was quite unexpected. If Quora can get me an opportunity to start a magazine then working on a startup can definitely open many doors.
9. Focus to get real work experience not just a piece of paper certifyingthat you worked for x months and you'll fetch great returns in the form of a successful career.
10. I am working on the post- "What HRs look in an ideal candidate- 21 Tips everyone must know in their 20s to fast track their Career Growth (Pattern Series- 3 of 11)". Interested people can followPsychological Patterns for getting notified when I publish it.

Read more about career advice at Career Consultant