I work out of a small office (~20 people) for a larger engineering company. Several of my coworkers were eventually hired after having dropped off their resumes in person. They had just moved here from different states, and also didn't know anyone at the office. They made a good impression with the receptionist, and I think my boss appreciated the slightly more personal nature of their approach - but we were actively hiring, and it's a smaller office.
There's something to be said for that - it's a good way to stand out from the pack, and if you're tactful and professional it shouldn't come off as desperate. I wouldn't ask to speak to employees, or the manager for that matter. But be friendly and brief with the receptionist, ask if you can leave a resume, and there's a good chance the boss will take a look at it.
It's been said but it bears repeating - do your research on the company and position you're applying for, and take the extra step to cater each resume to that specific position. Ten good resumes to ten different jobs will work better than one generic resume to a hundred positions.
Unfortunately, with larger companies, this approach may be more difficult if not impossible for the reasons already mentioned, but with smaller offices it can be very effective to get a foot in the door.