Should I be upfront about my intention during networking sessions?

I am a first year Masters' student and has been trying to network with people for full time recruitment next Summer/Fall. I understand that I missed the summer intern recruiting season for MBB and T2 this year and want to be more prepared next year. I am not from target and I know my chance of passing the resume screening will be low if I do not have people endorse me. So I have been reaching out to alum and people on Linkedin and had about 15 networking sessions with people from different consulting firms. I was doing it "the organic way", asking about their experience and trying to make it personal. Most of them seemed to be really nice but when I sent thank you emails and asked "it will be great if you can connect me with you colleagues who you think can be inspiring to me", I never got any response but one. Or if I asked at the end of the conversation, they would say let me think about it and I will get back to you later. I feel like my networking is not going anywhere and I am quite lost.

Should I just be upfront next time, say something like "I am reaching out, hoping to learn more about the company and your experience. And hopefully if you find me interesting and capable, you will feel comfortable referring me during the recruiting season"? I think inevitably the networking session in consulting industry itself is transactional to some degree and these people who agreed to meet with me probably knew my intention, especially if they just went through the whole recruiting process a year or two ago. Should I just be honest and verbal about my end goal so I don't waste their time or cause confusion?

How would you feel if someone reach out to you and approach the conversation like this? Thank you so much for any advice!