Cynthia,
Your film consists in the processed form of dyes, as the found in the C-41 colour-film.
However in your case those dyes are intended to form a grey hue in any case, whereas in the latter case those dyes are typically intended to form a coloured hue, aside of thase cases where a grey hue is part of the image.
Anyway, one effect of bad storage of C-41 colour films can be the disbalance of those dyes. Which would result in unwanted and not tro overcome hues at coloured and grey parts of the image, even though the film is not the end product, but typically copied to form a positive.
In case of those b&w films based on dyes such a dye disbalance is not to be expected, and if it would happen it would likely be of any effect in printing to b&w paper. In case of printing onto colour paper any resulting coloured hues could be filtered off.
Concerning labs, there is no technical reason to refuse films just because they are long beyond the expiry date as long as they are still the same process.
However there is one exception: most current C-41 films do not need any longer a certain treatment at the end of the process. Labs that run the newer process should reject the older films. Or warn the client, or even better end-process them apart.