Okay to reach out to firms advising internship deal?

Hello Everyone!

I am a student working in a Corporate Finance role for an industrial company in the south. I am going to be a Junior in the fall so I have been trying my best to secure an SA 2020 spot but have barely got back any responses and I am worried. In my internship, our finance team is exploring the option of buying another business and have had meetings with sell-side bankers pitching their client to us. Because I work in a small team and I think I've made a good impression on our CFO, I get to be involved on these meetings which has been a really cool learning experience.

I've introduced myself to the bankers as an intern. Many of them are very intelligent and from what I can tell, are people I'd respect and be motivated to work under. My question is, is it inappropriate if I reach out to them to grab coffee in hopes of getting a job? According to my bosses, it's totally fine but my team is pretty relaxed and they know what I'm gunning for and want to support me. I want to see from your guys' perspective if you would frown upon a student reaching out. Normally I'd say fuck it, and shoot my shot, but in these cases I don't want the bankers to feel obligated to respond in hopes of getting our business, especially when we might not follow through on some of the acquisitions.

Would love any insight on this!