FT8, no. I tested this extensively and a narrow bandwidth made no difference that I could detect.
RTTY, yes but only if a really strong station is right next to your frequency. To find out give it a try.
I run my FTdx-10 (similar to the FTdx-101D) on RTTY using the 500 Hz filter and have experimented with the 3000 Hz filter. So far I have not had a case where their was any difference in decode, but why run BW exceeding 400 Hz on RTTY?