It depends on the agent and the agency you intern at. I was a remote intern for close to a year and I'd told the agent I wasn't interested in going into publishing, I just wanted to catch a glimpse of what the industry is like from an agent's PoV and hopefully grow as a writer, so all of our conversations focused on the MSs I was asked to read and why they worked/didn't work and how, if it was my work, would I make it better. We discussed books and dissected themes and characters and market trends. He was very generous with his time and insight, and I came out of the internship a much better writer (I think).
His other remote intern was very interested in going into publishing, so what he did for her was more geared towards getting her an "in". He hooked her up with an indie bookshop. She worked at the bookshop and applied for paid positions at agencies, using the agent she interned for as a reference. After a few months at the bookshop, she got a job as an assistant at a different agency, worked there for close to a year, and now she's a full-time agent at another agency. So it can happen, it just depends on what you want and how good your relationship with the agent is.
