The answer here should be split into what's possible and what's likely.
Likely
Your application will, during its runtime, try to find the DLLs it expects to find. This means that the application is only concerned with the DLL files it knows about.
You can add as many other files to that folder as you want. Barring any name conflicts (which you already guarantee to not occur), the additional files do not matter to the application as it will never try to look up any of these files.
Possible
The above is simply default behavior. It is possible that the application actually looks inside the bin folder and iterates over its files (maybe only DLL files, maybe all files).
An example for why this would ever be done:
When you develop a mod for a game (depending on the game), you create a library. In some cases, your mod will include a DLL file (most often when it changes core game logic). Your mod is then installed in a specific directory. The base game will always look for any existing file in that directory (the mod you added), and try to incorporate it into its runtime.
It's not impossible that your application does something similar, e.g. looks for custom extensions at runtime and incorporates them using reflection.
However, it would be a bad (but again, not impossible) practice to expect these extensions to be put into the bin folder, as opposed to a custom folder.
So my answer is a combination of replies; ordered by desirability
- I would advise against using the bin folder for unrelated DLL files. I can't think of a good reason why it should ever be done. This smells of a blind company rule that foregoes any common sense or good practice.
- Since you seemingly cannot avoid putting the DLL in there, can you at least put it in a subfolder to segregate the DLL from the application DLLs? It's a matter of keeping things neatly ordered.
- For most applications, adding the DLL directly to the bin folder shouldn't matter on a technical level. It's a messy solution, but not inherently a problem by itself.
- If the application looks into its own bin folder at runtime, you can run into problems by adding the DLL and should clearly avoid it. However, I would expect such an application to document this feature. If it is never mentioned that the application does this, it seems fair to assume that it doesn't happen. Of course, that very much depends on your company's documentation quality and common coding practices.
TL;DR
It's a horrible solution. Depending on the application, it might create conflicts. It won't conflict for most standard applications that do not use reflection. It's still a horrible solution.