Assuming you mean bit depth (word length), then no, it really doesn't apply. Even if you're working on 8-bit material, the software is almost undoubtedly working in 32-BFP (or even up to 80-bit in the case of Samplitude and perhaps a few others).
Unless you mean sample rate -- There are a few plugs I've worked with that sound a bit different (well, "hardly" different, but perhaps a whisker different in the very top end) at higher rates or upsampled. But most of those allow for upsampling on the fly anyway.
Put me squarely in the "eh" category there...