I would suggest running some targeted experiments to get a better understanding of how the granularity of the fixed-point representation is going to affect your data. The most common effect that prompts people to post questions about “broken” interpolation is that there does not seem to be any interpolation at all, due to the coarse granularity.
GPUs offer copious single-precision throughput, so where the accuracy of the interpolation is even just potentially an issue, I always recommend approaching the issue from the other direction: First try manual interpolation using single-precision computation, it may already be fast enough. For a 1-D interpolation, only two fused multiply-adds are needed:
__forceinline__ float lerp (float a, float b, float t)
return fmaf (t, b, fmaf (-t, a, a));