Possibly, but they'll be 2m away from her in a big enough room and wearing ppe
I want to work at the hospital where you see this.
Medical secretaries are usually crammed in two to a room with just enough space to fit in two desks, two chairs, one shared filing cabinet and possibly a set of shelves. And other staff don't usually put on clinical equipment to drop off the bundles of files and the envelope with the tape (if it's not electronic).
You also have to get to the office in the first place, which involves walking in through the doors, along the corridors, in the lifts and sometimes walking directly through the clinic first. You have to go into a shared area to use the photocopier. You often need to take something into clinic or ask a question that cannot wait. Medical records people come in to collect files for admissions, other clinic appointments and to file the notes after they've been typed up and documents/test results added (not everything is done electronically in all places). There are meetings, helping out colleagues where they ask questions. There's leaving the office for lunch. Going back to the office afterwards. Speaking to people in person because not everybody has the ability to send emails and phone use in clinic isn't possible. Leaving the office at the end of the day to go home, travelling through the hospital and using the same lifts, corridors, stairs and doors that everybody else does.
You aren't in a little airtight bubble from 9am to 5pm. You cross paths with multiple people, both patients and staff, every single day. and that's even before you consider using public transport or a staff bus to get there or move between sites (as no secretary I've ever known would be paid enough to be able to afford the on site parking five days per week).
It's always been an inherently social job.
However, if there is a significant number of secretaries refusing to be vaccinated, they'll end up doing what was initially tried around 15 years ago - record things electronically and give them to overseas transcription services whilst the medical staff have to enter much of the communications themselves. Much cheaper and less risk from people wanting to wait 10, 15 or 20 years (so until retirement/not at all really) before taking steps to protect the other people they will be in close proximity to at every point of the day.